Underwater Image Restoration Based on Wavelet Fusion and Reweighted Graph Total Variation Prior

Underwater Image Restoration Based on Wavelet Fusion and Reweighted Graph Total Variation Prior | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Underwater Image Restoration Based on Wavelet Fusion and Reweighted Graph Total Variation Prior Fuyao Bai, Congzheng Wang, Chuncheng Feng, Wanqi Gong, Lei Liu, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1624223/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract To solve the problems of color distortion and blur in underwater images, the paper compensates the loss of the red channel after color correcting process, and uses the image information itself as the basis to estimate the fuzzy kernel to restore the final image. Firstly, stretch image gray value range to correct color cast and improve contrast. The redundant noise in red channel of the image is removed by median filtering to reduce interference. Subsequently, the pre-processed red channel and green channel of the image are split into high frequency and low frequency components by using SYM4 as the wavelet basis, and then the fusion is performed respectively. The new red channel after information compensation is obtained by reconstruction based on inverse wavelet transform. Then, the algorithm of the reweighted graph total variation prior combined with multi-resolution image pyramiding strategy is used to obtain the fuzzy kernel estimation. Finally, the image is restored by using a non-blind recovery algorithm based on ring suppression, which effectively suppresses the ringing effect while adequately preserving details. The simulation results of the proposed algorithm and several classical algorithms show that the proposed algorithm can effectively remove blur and improve image clarity while enhancing image and correcting color deviation. underwater image processing wavelet fusion the reweighted graph total variation prior color correction deblurring Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1 Introduction With the deepening of the exploration and development of the underwater world, the fields of underwater detection, underwater archaeology and aquatic life protection are developing rapidly. As an extension of human vision, underwater optical image is an important means of recording and transmitting underwater information. Different from the terrestrial environment, the underwater imaging process is affected by a variety of unfavorable factors such as scattering effect and selective absorption characteristics, which result in problems such as atomization, lack of contrast and color distortion. In addition, turbulence, target movement, and shaking of imaging equipment can blur images [ 1 ] . The degradation of underwater images directly affects its application and brings obstacles to the smooth development of underwater work. Therefore, improving the underwater image processing technology and obtaining high-quality underwater image is a top priority. Underwater image restoration is based on imaging model, prior knowledge and other information. Among them, linear image degradation model and Jaffe-McGlamery underwater imaging model [ 2 ] are two commonly used underwater image degradation models. In 1969, W. H. wells [ 3 ] obtained the point spread function by calculating the volume scattering function under the condition of small-angle scattering approximation. In 2001, Liu et al. [ 4 ] conducted the water tank experiments with slit images to estimate the point spread function based on the image transmission theory. In 2005, Schechner et al. [ 5 ] restored visibility by using the difference between two images that are maximum and minimum affected by polarized light at the same azimuth acquired by a polarizer under natural light. In 2007, Hou et al. [ 6 ] incorporated the underwater optical characteristics into the system response function, which was obtained the system response function of the medium by the Wells experiment. In 2010, Carlevaris-Bianco et al. [ 7 ] estimated scene depth by using attenuation differences between color channels during underwater imaging. In 2013, Drews et al. [ 8 ] proposed the underwater dark channel prior algorithm, directly discarding the red channel information and only using blue and green channels to obtain the transmittance map of underwater image. In 2015, Galdran et al. [ 9 ] proposed the red-channel prior algorithm, replacing the original red channel with the reverse channel of the red channel. In 2016, Chong-Yi Li et al. [ 10 ] proposed an underwater image defogging algorithm based on minimum information loss and histogram distribution prior, which estimated the transmittance map of the red channel by minimizing information loss. In 2017, Berman et al. [ 11 ] simplified the underwater image restoration problem as all color channels had the same attenuation coefficient by using the ratio of attenuation coefficients between channels. In 2018, Xieet al. [ 12 ] obtained optical parameters of water bodies by combining marine optical theory and dark channel prior algorithm to estimate global background light intensity and correct transmittance values, but this method is only applicable to shallow water areas. In 2020, Lin et al. [ 13 ] proposed an underwater image restoration algorithm based on modified scattering model and dark channel prior, which can effectively restore image color and detail information, but it does not consider the influence of factors such as small angle scattering and artificial light sources. With the development of artificial intelligence, machine learning has also been applied to underwater image restoration. In 2016, Shin et al. [ 14 ] estimated the background light and transmittance of underwater images with a general convolutional neural network structure. In 2018, Hou et al. [ 15 ] proposed the underwater residual convolutional neural network model, which can conduct residual learning of underwater image transmission and scene at the same time. In 2019, Lu et al. [ 16 ] proposed a MCycleGAN model using multi-scale cycle generative adversarial networks, which realized the combination of dark channel prior and cycle generative adversarial networks. In 2020, Li et al. [ 17 ] proposed UWCNN, an image enhancement convolutional neural network model based on underwater scenes, and solved the parameter estimation problem of underwater imaging model by using synthetic underwater images of different degradation degrees under various water types as an important reference for network training and image quality evaluation. Early underwater image restoration mainly focused on the construction of degradation models and their parameter estimation. Researchers tried a variety of measurement experiments, but such methods were affected by water characteristics and shooting conditions that the accuracy of the measurement was difficult to guarantee. The introduction of polarization technology improves the restoration effect effectively, but it depends on polarization equipment. And dark channel prior algorithm [ 18 ] expands the idea for underwater image restoration. As it evolved, deep learning began to be used. However, this method needs a large number of data sets as the support, and the network model trained is usually poor applicability. To sum up, the existing algorithms have a lot of room for improvement in the aspects of effectiveness, robustness and effectiveness. In order to correct the color deviation of underwater images and improve their clarity, a restoration algorithm based on wavelet fusion and the reweighted graph total variation prior is proposed in this paper. Among them, we split and fused the red channel and the green channel to obtain the compensated red channel by using the wavelet transform, and tried to estimate the point spread function by using the prior of the reweighted graph total variation [ 19 ] . The experimental results show that the proposed algorithm has a good comprehensive effect on color correction, clarity improvement and blur removal. 2 Algorithm Principle First, we stretch the gray values of color channels of the underwater image respectively within the limited range, and then use median filtering algorithm to de-noise the red channel. Next, the loss of information in the red channel is compensated by capturing details from the green channel. We used SYM4 as the wavelet basis to split red channel and green channel images. For low-frequency components, the fusion rule based on the mean value is used, while for high-frequency components, the fusion rule based on the regional energy is used. After that, new red channel with information compensation is obtained. Then, we use the blind restoration model based on the prior of the reweighted graph total variation [ 19 ] and combine it with the multi-resolution pyramid strategy to obtain the fuzzy kernel estimates iteratively layer by layer from low resolution to high resolution. After estimating the fuzzy kernel, the final image is restored by a non-blind recovery algorithm based on ringing suppression [ 20 ] . The entire process of the algorithm is shown in the Fig. 1. Figure 1. Algorithm flow chart 2.1 Contrast stretching In underwater imaging, the energy attenuation of light will occur to different degrees due to the absorption characteristics of water during the propagation process. The wavelength of red light is longer than that of green light and blue light, and it is always completely absorbed in close proximity, so the underwater image is generally biased towards blue-green. We solve the problem of color deviation and insufficient contrast by stretching the gray range of the underwater image. In order to reduce the influence of extreme gray values, we select the gray values from the top 0.5–95.5% when gray values are arranged from small to large of each color channel as the stretching interval [ 21 ] . The specific stretching formula is: \(I_{1}^{c}=\frac{{{I^c} - I_{{\hbox{min} }}^{c}}}{{I_{{\hbox{max} }}^{c} - I_{{\hbox{min} }}^{c}}} \times 255\) \(\left( 1 \right)\) Where: represents different color channels; \({I_1}\) is the output image; is the original image; \({I_{\hbox{max} }}\) is the gray value of the top 0.5% ; \({I_{\hbox{min} }}\) is the gray value of the top 95.5%. Since the grayscale values of red channel are generally low, stretching it introduces a lot of noise. We use median filtering to reduce the adverse effects of the noise problem, but it also loses more detail of the red channel in the process. 2.2 Wavelet fusion After selecting the appropriate decomposition level and wavelet function, we can use the wavelet transform to split the image into low-frequency components containing the image infra structure information and high-frequency components containing the image detail information. Since the image information is allocated to different components according to the wavelet coefficient, we deal with different wavelet coefficients and reconstruct them based on the inverse wavelet transform to obtain the final image. The two-dimensional discrete wavelet transform is used to process the digital image, that is, one-dimensional discrete wavelet transform is carried out in the row and column directions of the image respectively. The expression for the one-dimensional discrete wavelet transform is [ 22 ] : \({W_f}\left( {j,k} \right)={2^{ - \frac{j}{2}}}\sum\limits_{0}^{{N - 1}} {f\left( n \right)\psi \left( {{2^{ - j}}n - k} \right)}\) \(\left( 2 \right)\) Where: \({W_f}\left( { * , * } \right)\) is the wavelet coefficient; \(f\left( * \right)\) is the input signal; \(\psi \left( * \right)\) is the wavelet function; is the discretized scale parameter; is the discretized time delay parameter; is the total number of sampling points. Correspondingly, its inverse transformation expression is [ 22 ] : \(f\left( n \right)=\frac{1}{A}\sum\limits_{{j,k}} {{W_f}\left( {j,k} \right){\psi _{j,k}}\left( n \right)}\) \(\left( 3 \right)\) Where: is the boundary of the wavelet frame constituted by \({\psi _{j,k}}\left( t \right)\) . In this paper, we use sym4 as the wavelet basis to decompose the pre-processed red and green channel images into three layers. The low frequency and high frequency components are fused by the rule of mean value and the rule of region energy respectively. The fused components are reconstructed based on the inverse wavelet transform to obtain the red channel after information compensation. The algorithm based on the wavelet fusion is shown in the Fig. 2. Figure 2. Color correction flow chart 2.3 Deblurring In 2018, Bai et al. [ 19 ] found that the graph edge weights of the clear image presented a unique bimodal distribution different from it of the blurry image. The intermediate skeleton image, which retains the strong gradient and smoothen the minor details, still has this property. Therefore, the reweighted graph total variation prior (RGTV) is proposed to reconstruct the intermediate skeleton image from the fuzzy image by promoting the tendency of the graph edge weights to bimodal distribution, and then accurately estimate the fuzzy kernel. The prior of the reweighted graph total variation is defined as [ 19 ] : \({\left\| x \right\|_{RGTV}}=\sum\limits_{{i=1}}^{N} {\sum\limits_{{j=1}}^{N} {{\omega _{i,j}}\left( {{x_i},{x_j}} \right)} } \left| {{x_j} - {x_i}} \right|\) \(\left( 4 \right)\) Where: \(i,j\) represents the serial number of pixel points; is the total number of pixel points; is the gray value of pixel points; \(\omega\) is the edge weight of the graph. The blind restoration model based on the prior of RGTV is established as [ 19 ] : \(\hat {x},\hat {k}=\mathop {\arg {\kern 1pt} \hbox{min} }\limits_{{x,k}} \frac{1}{2}\left\| {x \otimes k - b} \right\|_{2}^{2}+\beta {\left\| x \right\|_{RGTV}}+\mu \left\| k \right\|_{2}^{2}\) \(\left( 5 \right)\) Where: is the intermediate skeleton image; is the point diffusion function; is the degraded image; \(\beta\) and \(\mu\) are two corresponding parameters. We obtain multi-resolution image pyramid by down-sampling and execute the whole algorithm in order from low resolution to high resolution. The final fuzzy kernel estimate and intermediate skeleton image are obtained by iterating to the highest resolution layer. In order to preserve the details and suppress the ringing effect better, we combine the obtained fuzzy kernel with the non-blind restoration algorithm based on ringing suppression [ 20 ] . First, the algorithms based on super-Laplacian prior [ 23 ] and based on L0 regularization prior [ 20 ] are used to obtain the restored image respectively. Then, we calculate the difference graph of two restored images and apply bilateral filtering algorithm to it. Finally, subtract the difference image after bilateral filtering from the image restored by using the algorithm based on super-Laplacian prior, and the result is the final restored image. The entire restoration process is shown in Fig. 3 . 3 Experiments And Analysis We carried out simulation experiments for self-defined underwater fuzzy images and real underwater fuzzy images, and compared the results of the proposed algorithm with those of several classical underwater image processing algorithms from two aspects of vision and evaluation indexes. Dark channel prior (DCP) algorithm [ 18 ] , underwater dark channel prior (UDCP) algorithm [ 8 ] , red channel prior (RDCP) algorithm [ 9 ] and Fusion algorithm [ 24 ] were included. All experiments were implemented in Matlab2018a, where the computer was configured as a 1.0GHz processor with 16GB of RAM. 3.1 Subjective analysis We selected two underwater images [ 25 ] with good quality and convolved them with two different self-defined fuzzy kernels to obtain self-defined underwater fuzzy images. In addition, we selected six underwater images [ 25 ] in different scenarios. The processing results of self-defined underwater fuzzy images and real underwater images are shown in Fig. 4 and Fig. 5 respectively. As can be seen from Fig. 4 , there are obvious blurring in the processing results of DCP, UDCP, RDCP, Fusion algorithms, while the clarity of images obtained by using the algorithm in this paper is significantly improved. In general, DCP, UDCP, and RDCP algorithms all have good defogging effect. However, the DCP algorithm does not consider the light attenuation, it cannot effectively correct the color deviation of images, and even aggravates it. UDCP algorithm is improved on the basis of DCP algorithm, but the overall brightness of processed images is generally low, and there is still a serious color deviation problem. Although RDCP algorithm compensates for red channel, processed images are biased to red tone. Fusion algorithm has a good effect on color restoration, but the processed images tend to be white on the whole, and the image clarity is low. In contrast, the proposed algorithm is better at comprehensively handling color deviation and blur than the rest of the algorithms. 3.2 Objective Analysis Three different evaluation indexes including UCIQE [ 26 ] , information entropy and average gradient [ 27 ] were used to objectively quantify the processing results. UCIQE is a kind of unreferenced underwater image quality evaluation index, which is a linear combination of chroma standard deviation, brightness contrast and saturation mean value in CIELab space. The larger the value is, the better the image quality is. From the perspective of information theory, information entropy measures the richness of information contained in an image. The larger the value of information entropy is, the more information and details the image contains. Average gradient is a commonly used evaluation index of image sharpness, which takes the average of the sum of the squares of the image gradients as the evaluation basis. The larger the value is, the higher the image sharpness is. The comparison results of the objective evaluation indexes are shown in Table 1 and Table 2 , and it can be seen from the data that the UCIQE, information entropy and average gradient scores of the proposed algorithm are mostly higher than those of the comparison algorithms, indicating that the image information restored by the proposed algorithm is more informative and detailed, that is to say, the algorithm can balance the contrast, chroma and saturation of the image in a better way. 4 Conclusion In order to solve the problems of color distortion, ambiguity and insufficient contrast of underwater image caused by scattering effect and absorption characteristics in the imaging process, an underwater restoration algorithm based on wavelet fusion and the prior of the reweighted graph total variation is proposed in this paper. The method firstly corrects the color deviation and improves the contrast of the image by stretching color channels, and obtains the compensated red channel by using median filtering and wavelet fusion. Then, the blind restoration model based on the prior of reweighted graph total variation is used to deblur the image. In order to reduce the impact of ringing effect and improve the accuracy of restoration, the algorithm based on the super Laplacian prior and the L0 regularization prior is used in the stage of non-blind restoration. Finally, we carried out comparative experiments to evaluate the proposed algorithm from both subjective and objective perspectives. Experimental results show that the comprehensive performance of the proposed algorithm is better than other algorithms in the aspects of color correction and blur removal. However, the running speed of this algorithm is slow and it is not suitable for real-time processing. In the future, we will further study how to improve the processing speed, and try to solve the non-uniform fuzzy problem by partition. Table 1 Self-defined blurred image processing results Algorithm NO. UCIQE IE AG NO. UCIQE IE AG Original image 0.56 7.13 2.35 0.54 7.08 2.08 DCP 0.55 6.96 2.28 0.54 6.91 2.02 UDCP ① 0.55 6.56 2.05 ③ 0.53 6.48 1.78 RDCP 0.61 7.23 2.69 0.60 7.25 2.48 Fusion 0.55 7.40 3.13 0.55 7.36 2.93 Proposed algorithm 0.63 7.60 5.95 0.63 7.66 5.13 Original image 0.56 7.57 2.49 0.55 7.54 2.21 DCP 0.59 7.27 2.76 0.59 7.22 2.50 UDCP ② 0.59 7.40 2.92 ④ 0.59 7.36 2.65 RDCP 0.57 7.45 2.52 0.57 7.43 2.26 Fusion 0.55 7.59 3.33 0.55 7.56 3.11 Proposed algorithm 0.59 7.84 6.21 0.59 7.84 5.02 Table 2 Real blurred image processing results Algorithm NO. UCIQE IE AG NO. UCIQE IE AG Original image 0.37 5.89 1.21 0.44 6.76 1.74 DCP 0.52 6.85 1.59 0.49 6.74 2.31 UDCP ① 0.54 7.00 1.74 ④ 0.55 6.70 2.44 RDCP 0.52 6.91 1.41 0.54 7.22 2.74 Fusion 0.45 6.88 2.70 0.50 7.31 4.45 Proposed algorithm 0.62 7.71 4.02 0.61 7.79 4.52 Original image 0.46 6.99 1.94 0.32 5.62 1.45 DCP 0.53 7.04 2.20 0.32 5.55 1.37 UDCP ② 0.60 7.29 2.52 ⑤ 0.32 5.55 1.38 RDCP 0.53 7.52 2.68 0.51 6.63 3.10 Fusion 0.50 7.39 4.24 0.41 6.93 5.03 Proposed algorithm 0.57 7.77 4.17 0.62 7.59 10.41 Original image 0.43 6.82 2.38 0.39 6.39 1.39 DCP 0.52 7.14 2.90 0.41 6.40 0.87 UDCP ③ 0.61 7.27 3.32 ⑥ 0.45 6.72 1.05 RDCP 0.57 7.37 2.87 0.55 7.13 1.31 Fusion 0.49 7.26 4.34 0.46 7.10 2.66 Proposed algorithm 0.60 7.70 5.41 0.65 7.67 4.92 References Yinjing GUO, Qi WU, Jiaojiao YUAN, Jiachen HOU, Wenhong LÜ. Research Progress on Underwater Optical Image Processing[J]. Journal of Electronics & Information Technology, 2021, 43(2): 426-435. Jaffe J S. 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Li, C. Guo, W. Ren, R. Cong, J. Hou, S. Kwong, D. Tao, “An Underwater Image Enhancement Benchmark Dataset and Beyond,” IEEE Trans. Image Process., vol. 29, pp.4376-4389, 2019. Yang M, Sowmya A. An underwater color image quality evaluation metric [J].IEEE Transactions on Image Processing, 2015, 24(12):6062-6071. He N, Wang J B, Zhang L L, et al. An improved fractional-order differentiation model for image denoising[J].Signal Processing, 2015,112:180-188. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1624223","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":104783823,"identity":"26eda365-046e-414f-82ea-bf200a8688ba","order_by":0,"name":"Fuyao Bai","email":"","orcid":"","institution":"University of Chinese Academy of Sciences","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Fuyao","middleName":"","lastName":"Bai","suffix":""},{"id":104783824,"identity":"c9d73a90-67b8-4fd3-8447-3bae19f5cceb","order_by":1,"name":"Congzheng 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Sciences","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Ke","middleName":"","lastName":"Zeng","suffix":""},{"id":104783831,"identity":"b74339d2-969a-402d-a5e0-3b8259555ca2","order_by":6,"name":"Chang Feng","email":"","orcid":"","institution":"Institute of Optics and Electronics, Chinese Academy of Sciences","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Chang","middleName":"","lastName":"Feng","suffix":""}],"badges":[],"createdAt":"2022-05-05 03:59:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1624223/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1624223/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":21448841,"identity":"dbaa4dd6-93ab-4e5b-8494-6c43d7c94e1a","added_by":"auto","created_at":"2022-05-13 19:17:37","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":59847,"visible":true,"origin":"","legend":"\u003cp\u003eAlgorithm flow chart\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-1624223/v1/fef779bd1b3ed546166f37fa.png"},{"id":21448844,"identity":"f1e17104-1734-4574-a7f1-3e37ece6b974","added_by":"auto","created_at":"2022-05-13 19:17:37","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":99780,"visible":true,"origin":"","legend":"\u003cp\u003eColor correction flow chart\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-1624223/v1/e3cb4d986efeba0c2614adb9.png"},{"id":21449955,"identity":"bff350eb-043c-463e-84d9-4256565df4b6","added_by":"auto","created_at":"2022-05-13 19:27:37","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":80861,"visible":true,"origin":"","legend":"\u003cp\u003eRestoration algorithm flow chart\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-1624223/v1/24f1b6d8ffdea58cc0af6c39.png"},{"id":21449593,"identity":"79c88b07-6c82-411f-a132-da5687153bff","added_by":"auto","created_at":"2022-05-13 19:22:37","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":303937,"visible":true,"origin":"","legend":"\u003cp\u003eSelf-defined blurred image processing results\u003c/p\u003e\u003cp\u003e(a)Original image ,(b) Self-defined underwater blurry image, (c) dark channel prior algorithm ,(d) underwater dark channel prior algorithm ,(e) Red Channel Prior Algorithm ,(f) Image Fusion Algorithm ,(g) Algorithm of this article\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-1624223/v1/d3076c84c20893848d8f8687.png"},{"id":21449595,"identity":"75141eff-4f2a-4f9e-90da-876bbf76edb7","added_by":"auto","created_at":"2022-05-13 19:22:37","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":470156,"visible":true,"origin":"","legend":"\u003cp\u003eReal blurred image processing results\u003c/p\u003e\u003cp\u003e(a) Original image ,(b) dark channel prior algorithm ,(c) underwater dark channel prior algorithm ,(d) red channel prior Algorithm ,(e) Image fusion algorithm ,(f) Algorithm of this article\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-1624223/v1/851d420be5f6ee694adb5aff.png"},{"id":34435739,"identity":"51da5e30-d21f-4aea-b0a0-617cc09f64e2","added_by":"auto","created_at":"2023-03-17 19:20:02","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1532607,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1624223/v1/20054d91-22b0-4c42-8a9d-a3b30e84fa76.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Underwater Image Restoration Based on Wavelet Fusion and Reweighted Graph Total Variation Prior","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eWith the deepening of the exploration and development of the underwater world, the fields of underwater detection, underwater archaeology and aquatic life protection are developing rapidly. As an extension of human vision, underwater optical image is an important means of recording and transmitting underwater information. Different from the terrestrial environment, the underwater imaging process is affected by a variety of unfavorable factors such as scattering effect and selective absorption characteristics, which result in problems such as atomization, lack of contrast and color distortion. In addition, turbulence, target movement, and shaking of imaging equipment can blur images\u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/sup\u003e. The degradation of underwater images directly affects its application and brings obstacles to the smooth development of underwater work. Therefore, improving the underwater image processing technology and obtaining high-quality underwater image is a top priority.\u003c/p\u003e \u003cp\u003eUnderwater image restoration is based on imaging model, prior knowledge and other information. Among them, linear image degradation model and Jaffe-McGlamery underwater imaging model\u003csup\u003e[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]\u003c/sup\u003e are two commonly used underwater image degradation models. In 1969, W. H. wells\u003csup\u003e[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]\u003c/sup\u003e obtained the point spread function by calculating the volume scattering function under the condition of small-angle scattering approximation. In 2001, Liu et al.\u003csup\u003e[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]\u003c/sup\u003e conducted the water tank experiments with slit images to estimate the point spread function based on the image transmission theory. In 2005, Schechner et al.\u003csup\u003e[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]\u003c/sup\u003e restored visibility by using the difference between two images that are maximum and minimum affected by polarized light at the same azimuth acquired by a polarizer under natural light. In 2007, Hou et al. \u003csup\u003e[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/sup\u003e incorporated the underwater optical characteristics into the system response function, which was obtained the system response function of the medium by the Wells experiment. In 2010, Carlevaris-Bianco et al. \u003csup\u003e[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]\u003c/sup\u003eestimated scene depth by using attenuation differences between color channels during underwater imaging. In 2013, Drews et al. \u003csup\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/sup\u003e proposed the underwater dark channel prior algorithm, directly discarding the red channel information and only using blue and green channels to obtain the transmittance map of underwater image. In 2015, Galdran et al.\u003csup\u003e[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/sup\u003e proposed the red-channel prior algorithm, replacing the original red channel with the reverse channel of the red channel. In 2016, Chong-Yi Li et al.\u003csup\u003e[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/sup\u003e proposed an underwater image defogging algorithm based on minimum information loss and histogram distribution prior, which estimated the transmittance map of the red channel by minimizing information loss. In 2017, Berman et al.\u003csup\u003e[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003c/sup\u003e simplified the underwater image restoration problem as all color channels had the same attenuation coefficient by using the ratio of attenuation coefficients between channels. In 2018, Xieet al.\u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/sup\u003e obtained optical parameters of water bodies by combining marine optical theory and dark channel prior algorithm to estimate global background light intensity and correct transmittance values, but this method is only applicable to shallow water areas. In 2020, Lin et al.\u003csup\u003e[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]\u003c/sup\u003e proposed an underwater image restoration algorithm based on modified scattering model and dark channel prior, which can effectively restore image color and detail information, but it does not consider the influence of factors such as small angle scattering and artificial light sources.\u003c/p\u003e \u003cp\u003eWith the development of artificial intelligence, machine learning has also been applied to underwater image restoration. In 2016, Shin et al.\u003csup\u003e[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]\u003c/sup\u003e estimated the background light and transmittance of underwater images with a general convolutional neural network structure. In 2018, Hou et al. \u003csup\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]\u003c/sup\u003e proposed the underwater residual convolutional neural network model, which can conduct residual learning of underwater image transmission and scene at the same time. In 2019, Lu et al. \u003csup\u003e[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]\u003c/sup\u003e proposed a MCycleGAN model using multi-scale cycle generative adversarial networks, which realized the combination of dark channel prior and cycle generative adversarial networks. In 2020, Li et al. \u003csup\u003e[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]\u003c/sup\u003e proposed UWCNN, an image enhancement convolutional neural network model based on underwater scenes, and solved the parameter estimation problem of underwater imaging model by using synthetic underwater images of different degradation degrees under various water types as an important reference for network training and image quality evaluation.\u003c/p\u003e \u003cp\u003eEarly underwater image restoration mainly focused on the construction of degradation models and their parameter estimation. Researchers tried a variety of measurement experiments, but such methods were affected by water characteristics and shooting conditions that the accuracy of the measurement was difficult to guarantee. The introduction of polarization technology improves the restoration effect effectively, but it depends on polarization equipment. And dark channel prior algorithm \u003csup\u003e[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]\u003c/sup\u003e expands the idea for underwater image restoration. As it evolved, deep learning began to be used. However, this method needs a large number of data sets as the support, and the network model trained is usually poor applicability. To sum up, the existing algorithms have a lot of room for improvement in the aspects of effectiveness, robustness and effectiveness. In order to correct the color deviation of underwater images and improve their clarity, a restoration algorithm based on wavelet fusion and the reweighted graph total variation prior is proposed in this paper. Among them, we split and fused the red channel and the green channel to obtain the compensated red channel by using the wavelet transform, and tried to estimate the point spread function by using the prior of the reweighted graph total variation \u003csup\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e. The experimental results show that the proposed algorithm has a good comprehensive effect on color correction, clarity improvement and blur removal.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"2 Algorithm Principle","content":"\u003cp\u003eFirst, we stretch the gray values of color channels of the underwater image respectively within the limited range, and then use median filtering algorithm to de-noise the red channel. Next, the loss of information in the red channel is compensated by capturing details from the green channel. We used SYM4 as the wavelet basis to split red channel and green channel images. For low-frequency components, the fusion rule based on the mean value is used, while for high-frequency components, the fusion rule based on the regional energy is used. After that, new red channel with information compensation is obtained. Then, we use the blind restoration model based on the prior of the reweighted graph total variation\u003csup\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e and combine it with the multi-resolution pyramid strategy to obtain the fuzzy kernel estimates iteratively layer by layer from low resolution to high resolution. After estimating the fuzzy kernel, the final image is restored by a non-blind recovery algorithm based on ringing suppression\u003csup\u003e[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/sup\u003e. The entire process of the algorithm is shown in the Fig.\u0026nbsp;1.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;1. Algorithm flow chart\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Contrast stretching\u003c/h2\u003e \u003cp\u003eIn underwater imaging, the energy attenuation of light will occur to different degrees due to the absorption characteristics of water during the propagation process. The wavelength of red light is longer than that of green light and blue light, and it is always completely absorbed in close proximity, so the underwater image is generally biased towards blue-green. We solve the problem of color deviation and insufficient contrast by stretching the gray range of the underwater image. In order to reduce the influence of extreme gray values, we select the gray values from the top 0.5\u0026ndash;95.5% when gray values are arranged from small to large of each color channel as the stretching interval\u003csup\u003e[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]\u003c/sup\u003e. The specific stretching formula is:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(I_{1}^{c}=\\frac{{{I^c} - I_{{\\hbox{min} }}^{c}}}{{I_{{\\hbox{max} }}^{c} - I_{{\\hbox{min} }}^{c}}} \\times 255\\)\u003c/span\u003e \u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\left( 1 \\right)\\)\u003c/span\u003e \u003c/span\u003e \u003c/p\u003e \u003cp\u003eWhere:\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003erepresents different color channels;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_1}\\)\u003c/span\u003e\u003c/span\u003eis the output image;\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003eis the original image;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_{\\hbox{max} }}\\)\u003c/span\u003e\u003c/span\u003eis the gray value of the top 0.5% ;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({I_{\\hbox{min} }}\\)\u003c/span\u003e\u003c/span\u003eis the gray value of the top 95.5%.\u003c/p\u003e \u003cp\u003eSince the grayscale values of red channel are generally low, stretching it introduces a lot of noise. We use median filtering to reduce the adverse effects of the noise problem, but it also loses more detail of the red channel in the process.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Wavelet fusion\u003c/h2\u003e \u003cp\u003e After selecting the appropriate decomposition level and wavelet function, we can use the wavelet transform to split the image into low-frequency components containing the image infra structure information and high-frequency components containing the image detail information. Since the image information is allocated to different components according to the wavelet coefficient, we deal with different wavelet coefficients and reconstruct them based on the inverse wavelet transform to obtain the final image. The two-dimensional discrete wavelet transform is used to process the digital image, that is, one-dimensional discrete wavelet transform is carried out in the row and column directions of the image respectively. The expression for the one-dimensional discrete wavelet transform is \u003csup\u003e[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/sup\u003e:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({W_f}\\left( {j,k} \\right)={2^{ - \\frac{j}{2}}}\\sum\\limits_{0}^{{N - 1}} {f\\left( n \\right)\\psi \\left( {{2^{ - j}}n - k} \\right)}\\)\u003c/span\u003e \u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\left( 2 \\right)\\)\u003c/span\u003e \u003c/span\u003e \u003c/p\u003e \u003cp\u003eWhere:\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({W_f}\\left( { * , * } \\right)\\)\u003c/span\u003e\u003c/span\u003eis the wavelet coefficient;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(f\\left( * \\right)\\)\u003c/span\u003e\u003c/span\u003eis the input signal;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\psi \\left( * \\right)\\)\u003c/span\u003e\u003c/span\u003eis the wavelet function;\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003eis the discretized scale parameter;\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003eis the discretized time delay parameter;\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003eis the total number of sampling points.\u003c/p\u003e \u003cp\u003eCorrespondingly, its inverse transformation expression is \u003csup\u003e[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/sup\u003e:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(f\\left( n \\right)=\\frac{1}{A}\\sum\\limits_{{j,k}} {{W_f}\\left( {j,k} \\right){\\psi _{j,k}}\\left( n \\right)}\\)\u003c/span\u003e \u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\left( 3 \\right)\\)\u003c/span\u003e \u003c/span\u003e \u003c/p\u003e \u003cp\u003eWhere:\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003eis the boundary of the wavelet frame constituted by\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\psi _{j,k}}\\left( t \\right)\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eIn this paper, we use sym4 as the wavelet basis to decompose the pre-processed red and green channel images into three layers. The low frequency and high frequency components are fused by the rule of mean value and the rule of region energy respectively. The fused components are reconstructed based on the inverse wavelet transform to obtain the red channel after information compensation. The algorithm based on the wavelet fusion is shown in the Fig.\u0026nbsp;2.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;2. Color correction flow chart\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Deblurring\u003c/h2\u003e \u003cp\u003eIn 2018, Bai et al. \u003csup\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e found that the graph edge weights of the clear image presented a unique bimodal distribution different from it of the blurry image. The intermediate skeleton image, which retains the strong gradient and smoothen the minor details, still has this property. Therefore, the reweighted graph total variation prior (RGTV) is proposed to reconstruct the intermediate skeleton image from the fuzzy image by promoting the tendency of the graph edge weights to bimodal distribution, and then accurately estimate the fuzzy kernel.\u003c/p\u003e \u003cp\u003eThe prior of the reweighted graph total variation is defined as\u003csup\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({\\left\\| x \\right\\|_{RGTV}}=\\sum\\limits_{{i=1}}^{N} {\\sum\\limits_{{j=1}}^{N} {{\\omega _{i,j}}\\left( {{x_i},{x_j}} \\right)} } \\left| {{x_j} - {x_i}} \\right|\\)\u003c/span\u003e \u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\left( 4 \\right)\\)\u003c/span\u003e \u003c/span\u003e \u003c/p\u003e \u003cp\u003eWhere:\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i,j\\)\u003c/span\u003e\u003c/span\u003erepresents the serial number of pixel points;\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003eis the total number of pixel points;\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003eis the gray value of pixel points;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\omega\\)\u003c/span\u003e\u003c/span\u003e is the edge weight of the graph.\u003c/p\u003e \u003cp\u003eThe blind restoration model based on the prior of RGTV is established as\u003csup\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e:\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\hat {x},\\hat {k}=\\mathop {\\arg {\\kern 1pt} \\hbox{min} }\\limits_{{x,k}} \\frac{1}{2}\\left\\| {x \\otimes k - b} \\right\\|_{2}^{2}+\\beta {\\left\\| x \\right\\|_{RGTV}}+\\mu \\left\\| k \\right\\|_{2}^{2}\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left( 5 \\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eWhere:\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003eis the intermediate skeleton image;\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003eis the point diffusion function;\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e is the degraded image;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\beta\\)\u003c/span\u003e\u003c/span\u003eand\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu\\)\u003c/span\u003e\u003c/span\u003eare two corresponding parameters.\u003c/p\u003e \u003cp\u003eWe obtain multi-resolution image pyramid by down-sampling and execute the whole algorithm in order from low resolution to high resolution. The final fuzzy kernel estimate and intermediate skeleton image are obtained by iterating to the highest resolution layer. In order to preserve the details and suppress the ringing effect better, we combine the obtained fuzzy kernel with the non-blind restoration algorithm based on ringing suppression\u003csup\u003e[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/sup\u003e. First, the algorithms based on super-Laplacian prior \u003csup\u003e[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]\u003c/sup\u003e and based on L0 regularization prior \u003csup\u003e[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/sup\u003e are used to obtain the restored image respectively. Then, we calculate the difference graph of two restored images and apply bilateral filtering algorithm to it. Finally, subtract the difference image after bilateral filtering from the image restored by using the algorithm based on super-Laplacian prior, and the result is the final restored image. The entire restoration process is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3 Experiments And Analysis","content":"\u003cp\u003eWe carried out simulation experiments for self-defined underwater fuzzy images and real underwater fuzzy images, and compared the results of the proposed algorithm with those of several classical underwater image processing algorithms from two aspects of vision and evaluation indexes. Dark channel prior (DCP) algorithm \u003csup\u003e[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]\u003c/sup\u003e, underwater dark channel prior (UDCP) algorithm \u003csup\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/sup\u003e, red channel prior (RDCP) algorithm \u003csup\u003e[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/sup\u003e and Fusion algorithm \u003csup\u003e[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]\u003c/sup\u003e were included. All experiments were implemented in Matlab2018a, where the computer was configured as a 1.0GHz processor with 16GB of RAM.\u003c/p\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Subjective analysis\u003c/h2\u003e \u003cp\u003eWe selected two underwater images\u003csup\u003e[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/sup\u003e with good quality and convolved them with two different self-defined fuzzy kernels to obtain self-defined underwater fuzzy images. In addition, we selected six underwater images\u003csup\u003e[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/sup\u003e in different scenarios. The processing results of self-defined underwater fuzzy images and real underwater images are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e5\u003c/span\u003e respectively. As can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e4\u003c/span\u003e, there are obvious blurring in the processing results of DCP, UDCP, RDCP, Fusion algorithms, while the clarity of images obtained by using the algorithm in this paper is significantly improved. In general, DCP, UDCP, and RDCP algorithms all have good defogging effect. However, the DCP algorithm does not consider the light attenuation, it cannot effectively correct the color deviation of images, and even aggravates it. UDCP algorithm is improved on the basis of DCP algorithm, but the overall brightness of processed images is generally low, and there is still a serious color deviation problem. Although RDCP algorithm compensates for red channel, processed images are biased to red tone. Fusion algorithm has a good effect on color restoration, but the processed images tend to be white on the whole, and the image clarity is low. In contrast, the proposed algorithm is better at comprehensively handling color deviation and blur than the rest of the algorithms.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Objective Analysis\u003c/h2\u003e \u003cp\u003eThree different evaluation indexes including UCIQE\u003csup\u003e[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]\u003c/sup\u003e, information entropy and average gradient\u003csup\u003e[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]\u003c/sup\u003e were used to objectively quantify the processing results. UCIQE is a kind of unreferenced underwater image quality evaluation index, which is a linear combination of chroma standard deviation, brightness contrast and saturation mean value in CIELab space. The larger the value is, the better the image quality is. From the perspective of information theory, information entropy measures the richness of information contained in an image. The larger the value of information entropy is, the more information and details the image contains. Average gradient is a commonly used evaluation index of image sharpness, which takes the average of the sum of the squares of the image gradients as the evaluation basis. The larger the value is, the higher the image sharpness is. The comparison results of the objective evaluation indexes are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, and it can be seen from the data that the UCIQE, information entropy and average gradient scores of the proposed algorithm are mostly higher than those of the comparison algorithms, indicating that the image information restored by the proposed algorithm is more informative and detailed, that is to say, the algorithm can balance the contrast, chroma and saturation of the image in a better way.\u003c/p\u003e \u003c/div\u003e"},{"header":"4 Conclusion","content":"\u003cp\u003eIn order to solve the problems of color distortion, ambiguity and insufficient contrast of underwater image caused by scattering effect and absorption characteristics in the imaging process, an underwater restoration algorithm based on wavelet fusion and the prior of the reweighted graph total variation is proposed in this paper. The method firstly corrects the color deviation and improves the contrast of the image by stretching color channels, and obtains the compensated red channel by using median filtering and wavelet fusion. Then, the blind restoration model based on the prior of reweighted graph total variation is used to deblur the image. In order to reduce the impact of ringing effect and improve the accuracy of restoration, the algorithm based on the super Laplacian prior and the L0 regularization prior is used in the stage of non-blind restoration. Finally, we carried out comparative experiments to evaluate the proposed algorithm from both subjective and objective perspectives. Experimental results show that the comprehensive performance of the proposed algorithm is better than other algorithms in the aspects of color correction and blur removal. However, the running speed of this algorithm is slow and it is not suitable for real-time processing. In the future, we will further study how to improve the processing speed, and try to solve the non-uniform fuzzy problem by partition.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSelf-defined blurred image processing results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAlgorithm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNO.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUCIQE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAG\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNO.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eUCIQE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eIE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eAG\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOriginal image\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2.08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eUDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e①\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e③\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1.78\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2.48\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFusion\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2.93\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProposed algorithm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.63\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e7.60\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e5.95\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.63\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e7.66\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e5.13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOriginal image\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2.21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2.50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eUDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e②\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e④\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2.65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFusion\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e3.11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProposed algorithm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.59\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e7.84\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e6.21\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.59\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e7.84\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e5.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eReal blurred image processing results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAlgorithm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNO.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUCIQE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAG\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNO.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eUCIQE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eIE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eAG\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOriginal image\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1.74\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eUDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e①\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e④\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2.44\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2.74\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFusion\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e4.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProposed algorithm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.62\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e7.71\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e4.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.61\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e7.79\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e4.52\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOriginal image\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e5.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e5.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1.37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eUDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e②\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.60\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e⑤\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e5.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1.38\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e3.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFusion\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e5.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProposed algorithm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e7.77\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e4.17\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.62\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e7.59\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e10.41\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOriginal image\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1.39\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.87\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eUDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e③\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.61\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e⑥\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRDCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e1.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFusion\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e2.66\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProposed algorithm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e7.70\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e5.41\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.65\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e7.67\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e4.92\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eYinjing GUO, Qi WU, Jiaojiao YUAN, Jiachen HOU, Wenhong L\u0026Uuml;. Research Progress on Underwater Optical Image Processing[J]. Journal of Electronics \u0026amp; Information Technology, 2021, 43(2): 426-435. \u003c/li\u003e\n\u003cli\u003eJaffe J S. Computer modeling and the design of optimal underwater imaging systems[J]. IEEE Journal of Oceanic Engineering, 1990, 15(2):101-111.\u003c/li\u003e\n\u003cli\u003eWells W H. Loss of resolution in water as a result of multiple small-angle scattering[J]. JOSA, 1969, 59(6): 686-691.\u003c/li\u003e\n\u003cli\u003eLiu Z, Yu Y, Zhang K, et al. Underwater image transmission and blurred image restoration[J]. Optical Engineering, 2001, 40(6): 1125-1131.\u003c/li\u003e\n\u003cli\u003eSchechner Y Y, Karpel N. Recovery of underwater visibility and structure by polarization analysis[J]. IEEE Journal of oceanic engineering, 2005, 30(3): 570-587.\u003c/li\u003e\n\u003cli\u003eHou W, Gray D J, Weidemann A D, et al. Automated underwater image restoration and retrieval of related optical properties[C]//2007 IEEE international geoscience and remote sensing symposium. IEEE, 2007: 1889-1892.\u003c/li\u003e\n\u003cli\u003eCarlevaris-Bianco N, Mohan A, Eustice R M. Initial results in underwater single image dehazing[C]// Oceans. IEEE, 2010.\u003c/li\u003e\n\u003cli\u003eDrews J P, Nascimento E, Moraes F, et al. Transmission Estimation in Underwater Single Images[C]// IEEE International Conference on Computer Vision Workshops. IEEE, 2013.\u003c/li\u003e\n\u003cli\u003eGaldran, Adrian, Alvarez-Gila, et al. Automatic Red-Channel underwater image restoration[J]. Journal of visual communication \u0026amp; image representation, 2015.\u003c/li\u003e\n\u003cli\u003eLi C, Guo J, Cong R, et al. Underwater Image Enhancement by Dehazing With Minimum Information Loss and Histogram Distribution Prior[J]. IEEE Transactions on Image Processing, 2016, PP(99):1-1.\u003c/li\u003e\n\u003cli\u003eBerman D, Treibitz T, Avidan S. Diving into haze-lines: Color restoration of underwater images[C]//Proc. British Machine Vision Conference (BMVC). 2017, 1(2).\u003c/li\u003e\n\u003cli\u003eXie H, Peng G, Wang F, et al. Underwater image restoration based on background light estimation and dark channel prior[J]. Acta Optica Sinica, 2018, 38(1): 0101002.\u003c/li\u003e\n\u003cli\u003eLIN Sen, BAI Ying, LI Wentao, TANG Yandong. Underwater Image Restoration Based on the Modified Model and Dark Channel Prior. ROBOT, 2020, 42(4): 427-435,447.\u003c/li\u003e\n\u003cli\u003eShin Y S, Cho Y, Pandey G, et al. Estimation of ambient light and transmission map with common convolutional architecture[C]// Oceans. IEEE, 2016:1-7.\u003c/li\u003e\n\u003cli\u003eHou M, Liu R, Fan X, et al. Joint residual learning for underwater image enhancement[C]//2018 25th IEEE International Conference on Image Processing (ICIP). IEEE, 2018: 4043-4047.\u003c/li\u003e\n\u003cli\u003eLu J, Li N, Zhang S, et al. Multi-scale adversarial network for underwater image restoration[J]. Optics \u0026amp; Laser Technology, 2018, 110:105-113.\u003c/li\u003e\n\u003cli\u003eLi C, Anwar S, Porikli F. Underwater scene prior inspired deep underwater image and video enhancement[J]. Pattern Recognition, 2020, 98: 107038.\u003c/li\u003e\n\u003cli\u003eHe K, Sun J, Tang X. Single image haze removal using dark channel prior[J]. IEEE transactions on pattern analysis and machine intelligence, 2010, 33(12): 2341-2353.\u003c/li\u003e\n\u003cli\u003eBai Y, Cheung G, Liu X, et al. Graph-based blind image deblurring from a single photograph[J]. IEEE Transactions on Image Processing, 2018, 28(3): 1404-1418.\u003c/li\u003e\n\u003cli\u003ePan J, Zhe H, Su Z, et al. Deblurring Text Images via L0-Regularized Intensity and Gradient Prior[C]// 2014 IEEE Conference on Computer Vision and Pattern Recognition. IEEE, 2014.\u003c/li\u003e\n\u003cli\u003eHuang D M, Wang Y, Song W, Wang Z H, Du Y L. Underwater image enhancement method using adaptive histogram stretching in different color models[J]. Journal of Image and Graphics, 2018, 23(5): 640-651.\u003c/li\u003e\n\u003cli\u003eDU Shi-qiang, SONG Yu-kun, ZHANG Xuan, ZHANG Duo-li. Improved wavelet threshold denoising algorithm[J]. \u003cem\u003eMicroelectronics \u0026amp; Computer\u003c/em\u003e, 2021, 38(2): 40-46.\u003c/li\u003e\n\u003cli\u003eKrishnan D,Fergus R.Fast Image Deconvolution using Hyper-Laplacian Priors[C]// Advances in Neural Information Processing Systems 22: 23rd Annual Conference on Neural Information Processing Systems 2009. Proceedings of a meeting held 7-10 December 2009, Vancouver, British Columbia, Canada. Curran Associates Inc. 2009.\u003c/li\u003e\n\u003cli\u003eAncuti C O, Ancuti C, Vleeschouwer C D, et al. Color Balance and Fusion for Underwater Image Enhancement[J].IEEE Transactions on Image Processing, 2017, 27(99):379-393.\u003c/li\u003e\n\u003cli\u003eC. Li, C. Guo, W. Ren, R. Cong, J. Hou, S. Kwong, D. Tao, \u0026ldquo;An Underwater Image Enhancement Benchmark Dataset and Beyond,\u0026rdquo; IEEE Trans. Image Process., vol. 29, pp.4376-4389, 2019.\u003c/li\u003e\n\u003cli\u003eYang M, Sowmya A. An underwater color image quality evaluation metric [J].IEEE Transactions on Image Processing, 2015, 24(12):6062-6071.\u003c/li\u003e\n\u003cli\u003eHe N, Wang J B, Zhang L L, et al. An improved fractional-order differentiation model for image denoising[J].Signal Processing, 2015,112:180-188.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"underwater image processing, wavelet fusion, the reweighted graph total variation prior, color correction, deblurring","lastPublishedDoi":"10.21203/rs.3.rs-1624223/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1624223/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTo solve the problems of color distortion and blur in underwater images, the paper compensates the loss of the red channel after color correcting process, and uses the image information itself as the basis to estimate the fuzzy kernel to restore the final image. Firstly, stretch image gray value range to correct color cast and improve contrast. The redundant noise in red channel of the image is removed by median filtering to reduce interference. Subsequently, the pre-processed red channel and green channel of the image are split into high frequency and low frequency components by using SYM4 as the wavelet basis, and then the fusion is performed respectively. The new red channel after information compensation is obtained by reconstruction based on inverse wavelet transform. Then, the algorithm of the reweighted graph total variation prior combined with multi-resolution image pyramiding strategy is used to obtain the fuzzy kernel estimation. Finally, the image is restored by using a non-blind recovery algorithm based on ring suppression, which effectively suppresses the ringing effect while adequately preserving details. The simulation results of the proposed algorithm and several classical algorithms show that the proposed algorithm can effectively remove blur and improve image clarity while enhancing image and correcting color deviation.\u003c/p\u003e","manuscriptTitle":"Underwater Image Restoration Based on Wavelet Fusion and Reweighted Graph Total Variation Prior","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-05-13 19:17:35","doi":"10.21203/rs.3.rs-1624223/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7bac033f-24da-4534-9b95-c32fe7604a6f","owner":[],"postedDate":"May 13th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2023-03-17T19:19:48+00:00","versionOfRecord":[],"versionCreatedAt":"2022-05-13 19:17:35","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-1624223","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1624223","identity":"rs-1624223","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}