A Novel Electrocardiogram Denoising Method based on Convex fused-Lasso Denoising with Non-Convex Regularization and Wavelet/Total Variation

A Novel Electrocardiogram Denoising Method based on Convex fused-Lasso Denoising with Non-Convex Regularization and Wavelet/Total Variation | 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 A Novel Electrocardiogram Denoising Method based on Convex fused-Lasso Denoising with Non-Convex Regularization and Wavelet/Total Variation Abdallah Rezgui, Mourad Talbi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4540515/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 In this paper, we propose a new Electrocardiogram (ECG) denoising approach based on Convex fused lasso Denoising with non-convex regularization and Wavelet/Total Variation (WATV). This approach consists at first step of applying the Discrete Wavelet Transform (DWT) to the noisy ECG signal for obtaining a noisy approximation coefficient, cAb 1 and a noisy details coefficient, cDb 1 . The latter is denoised by soft thresholding and we obtain a denoised details coefficient, cDd 1 . The second step of this approach consists of applying the DWT to cAb 1 in order to obtain a noisy approximation coefficient, cAb 2 and a noisy details coefficient, cDb 2 . The latter is denoised by Convex fused lasso denoising with non-convex regularization and we obtain a denoised details coefficient, cDd 2 . The coefficient, cAb 2 , is denoised by WATV based denoising technique and we obtain a denoised coefficient, cAd 2 . The inverse of DWT is then applied to cDd 2 and cAd 2 in order to obtain a denoised approximation coefficient, cAd 1 . The inverse of DWT is again applied to cDd 1 and cAd 1 for obtaining finally a denoised ECG signal. The performance of this proposed approach is proved by the computation of SNR, the PSNR, the MSE, the Mean Absolute Error (MAE), and the Cross-Correlation (CC). Denoising ECG Convex fused lasso denoising with non-convex regularization Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction In the literature, there are many methods, such as the entropy, filtering, frequency analysis, time series analysis and models, such as auto regressive, and auto regressive moving average, spectral techniques, like power spectral density, wavelets, thresholding, denoising, Fourier transform, Hilbert–Huang transform, uncertainty principle, support vector machine, adaptive noise cancellation employed for enhancing the Signal-To-Noise Ratio (SNR) [ 1 ]. Signal denoising was conducted also via the Empirical Mode Decomposition (EMD), which is based on a local and adaptive technique in the frequency-time analysis. Some others are based on statistical model such as the so-called deep learning-based auto-encoder models [ 1 ]. Those models consist in regenerating a clean version of the analyzed signal from a degraded version based on an optimization process of an appropriate objective function. In the same category, Bayesian filters based models such as the extended Kalman filter, the extended Kalman smoother, and the unscented Kalman Filter are also known in bio-signals processing. Fuzzy models are also applied extensively, and also combined with neural networks [ 17 , 18 ] for signal processing. Also, we can mention the hybrid techniques developed by combining these ones. See Abhijith et al. [ 2 ], AlMahamdya and Riley [ 3 ] and Babatunde [ 4 ], Ben Mabrouk et al. [ 5 ]; Ho [ 6 ]; Mallat [ 7 ]; Xia and Suter [ 8 ]; Zemni et al. [ 9 , 10 ]. Wavelet techniques start primarily by decomposing the signal, deciding the type of thresholding and reconstructing the signal. Actually, wavelets was extended to multi-wavelets, which have shown some performance compared to existing techniques. Techniques based on wavelets/multi-wavelets including the mathematical theory of irregular functions to conduct signal processing, such as the estimation of Lipschitz exponent by means of wavelet/multi-wavelet coefficients or transform [ 1 ], performing the singularity detection, and therefore yields signal denoising algorithms employing the singularity detection. A thresholding process are permiting to de-noise the signal, and reconstructing the denoised version by simply applying the inverse multi-wavelet transform [ 1 ]. In this direction, Geronimo, Hardin and Massopust has introduced a technique for constructing translation and dilation invariant function spaces employing fractal functions defined by a certain class of iterated function systems [ 11 ]. Xia and collaborators (Xia [ 12 ]; Xia and Jiang [ 13 ]; Xia and Suter [ 8 ]) ameliorated such multi-wavelets by constructing a pre-filter design technique dealing with all decomposition steps for the discrete multi-wavelet transform, and appoximating a signal with the lowpass property. In this paper we propose a novel approach of Electrocardiogram (ECG) Denoising based on Wavelet/Total Variation (WATV) and Convex fused lasso Denoising with non-convex regularization. The rest of the paper is organized as follows: in section 2 , we will deal with our ECG denoising approach, proposed in this work. In section 3 , we will present results and discussion and finally we will conclude in section 4 . 2. The proposed ECG denoising technique In this paper, we propose a novel approach of Electrocardiogram (ECG) Denoising based on Wavelet/Total Variation (WATV) [ 14 ] and Convex fused lasso Denoising with non-convex regularization (Fig. 1 ). This approach consists at first step of applying the Discrete Wavelet Transform (DWT) to the noisy ECG signal for obtaining a noisy approximation coefficient, \({cAb}_{1}\) and a noisy details coefficient, \({cDb}_{1}\) . The latter is denoised by soft thresholding and we obtain a first denoised details coefficient, \({cDd}_{1}\) . The second step of this approach consists of applying the \(DWT\) to \({cAb}_{1}\) in order to obtain a second noisy approximation coefficient, \({cAb}_{2}\) and a second noisy details coefficient, \({cDb}_{2}\) . The latter is denoised by Convex fused lasso denoising with non-convex regularization [ 15 ] and we obtain a second denoised details coefficient, \({cDd}_{2}\) . The noisy approximation coefficient, \({cAb}_{2}\) , is denoised by WATV based denoising technique and we obtain a denoised approximation coefficient, \({cAd}_{2}\) . The inverse of \(DWT\) is then applied to \({cDd}_{2}\) and \({cAd}_{2}\) in order to obtain a denoised approximation coefficient, \({cAd}_{1}\) . The inverse of \(DWT\) is again applied to \({cDd}_{1}\) and \({cAd}_{1}\) for obtaining finally a denoised \(ECG\) signal. For the soft thresholding of \({cDb}_{1}\) , we use a threshold, thr (Fig. 1 ), which is expressed as follow: $$thr=\sigma \bullet \sqrt{2\bullet log\left(N\right)}$$ 1 Where N is the number of samples of \({cDb}_{1}\) and \(\sigma\) is the estimated noise level, and expressed as follow: $$\sigma =MAD\left(\left|c{D}_{1}\right|\right)/0.6745$$ 2 This estimated noise level, \(\sigma\) , is also used for the application of WATV [ 14 ] based denoising technique to \({cAb}_{2}\) . 3. Results and discussion For evaluating and testing the performance of our ECG denoising approach, we compared it the WATV based denoising technique [ 14 ], the Convex fused lasso denoising with non-convex regularization [ 15 ] and a statistical approach to signal denoising based on data-driven multiscale representation [ 16 ]. This comparison is performed by computing the Signal to Noise Ratio (SNR), the Peak SNR (PSNR), the Mean Square Error (MSE), the Mean Absolute Error (MAE) and the Cross-Correlation (CC), and this for five values of SNR before denoising, SNRi. These values are − 5dB, 0dB, 5dB, 10dB and 15dB and the results obtained from the previously mentioned denoising techniques, are listed in Table 1 . According to Table 1 , the best results are highlighted in blue color and in cases of SNRi = 5dB or SNRi = 10dB or SNRi = 15dB, they are obtained from the application of the proposed ECG denoising technique. Therefore, when the SNRi is higher (5dB or 10dB or 15dB), this proposed techni-que outperforms the other previously mentioned techniques used for this evaluation. In Figs. 2 –5, are illustrated some examples of ECG denoising by applying the proposed technique. According to these figures, the proposed technique permits to cancel the noise while conserving the original signals. 4. Conclusion In this paper, we propose a novel approach of Electrocardiogram (ECG) Denoising based on Wavelet/Total Variation (WATV) and Convex fused lasso Denoising with non-convex regularization. This approach consists at first step of applying the Discrete Wavelet Transform (DWT) to the noisy ECG signal for obtaining a noisy approximation coefficient, \({cAb}_{1}\) and a noisy details coefficient, \({cDb}_{1}\) . The latter is denoised by soft thresholding and we obtain a first denoised details coefficient, \({cDd}_{1}\) . The second step of this approach consists of applying the \(DWT\) to \({cAb}_{1}\) in order to obtain a second noisy approximation coefficient, \({cAb}_{2}\) and a second noisy details coefficient, \({cDb}_{2}\) . The latter is denoised by Convex fused lasso denoising with non-convex regularization and we obtain a second denoised details coefficient, \({cDd}_{2}\) . The noisy approximation coefficient, \({cAb}_{2}\) , is denoised by WATV based denoising technique and we obtain a denoised approximation coefficient, \({cAd}_{2}\) . The inverse of \(DWT\) is then applied to \({cDd}_{2}\) and \({cAd}_{2}\) in order to obtain a denoised approximation coefficient, \({cAd}_{1}\) . The inverse of \(DWT\) is again applied to \({cDd}_{1}\) and \({cAd}_{1}\) for obtaining finally a denoised \(ECG\) signal. The performance of this proposed approach is proved by the computation of the Signal to Noise Ratio (SNR), the Peak SNR (PSNR), the Mean Square Error ( \(MSE\) ), the Mean Absolute Error ( \(MAE\) ), and the Cross-Correlation ( \(CC\) ). In fact, when the SNRi is higher (5dB or 10dB or 15dB), this proposed technique outperforms the other previously mentioned techniques used for this evaluation, WATV based denoising technique, Convex fused lasso denoising with non-convex regularization and A statistical approach to signal denoising based on data-driven multiscale representation. Declarations Author Contribution Abdallah introduce the novel ECG denoising and Mourad Talbi make the different matlab simulations and the two authors wrote the main manuscript text. All authors reviewed the manuscript. Data availability The data that support the findings of this study are available from the corresponding author upon reasonable request. Competing Interest declaration There are no Competing Interests. Funding Declaration There was no Funding for this manuscript. References Malika Jallouli, Makerem Zemni, Anouar Ben Mabrouk, Mohamed Ali Mahjoub. Toward new multi-wavelets: associated filters and algorithms. Part I: theoretical framework and investigation of biomedical signals, ECG, and coronavirus cases. Soft Computing (2021) 25:14059–14079 https://doi.org/10.1007/s00500-021-06217-y Abhijith A, Ruban DP, Rajy X, Mareeta CP (2016) Review of signal processing techniques for detection of power quality events. Am J Eng Appl Sci 9(2):364–370 AlMahamdya M, Riley HB (2014) Performance study of different denoising methods for ECG signals. Procedia Comput Sci 37:325– 332 Babatunde SE (2012) A review of signal processing techniques for heart sound analysis in clinical diagnosis. J Med Eng Technol 36(6):303–307 Ben Mabrouk A, Kortas H, Dhifaoui Z (2008a) A wavelet support vector machine coupled method for time series prediction. Int J Wavelets Multiresolution Inf Process 6(6):1–17 Ho YF (2002) Singularity detection for regularity scalable image coding. Master thesis, Department of electronic and information engineering, Hong Kong University of Technology Mallat S (2008) A wavelet tour of signal processing, 3rd edn. Academic Press, Cambridge Xia X-G, Suter BW (1996) Vector-valued wavelets and vector filter banks. IEEE Trans Signal Process 44(3):508–518 Zemni M, Jallouli M, Ben Mabrouk A, Mahjoub MA (2019a) Explicit Haar–Schauder multiwavelet filters, and algorithms. Part II: relative entropy-based estimation for optimal modeling of biomedical signals. Int JWavelets Multiresolution Inf Process 17(05):1950038 Zemni M, Jallouli M, Ben Mabrouk A, Mahjoub MA (2019b) ECG signal processing with Haar–Schauder multiwavelet. In: Proceedings of the 9th international conference on information systems, and technologies—ICIST. https://doi.org/10.1145/3361570.3361611 Geronimo JS, Hardin DP, Massopust PR (1994) Fractal function and wavelet expansions based on several scaling functions. J Approx Theory 78:373–401 Xia X-G (1998) A new prefilter design for discrete multiwavelet transforms. IEEE Trans Signal Process 46:1558–1570 Xia T, Jiang Q (1999) Optimal multifilter banks: design, related symmetric extension transform, and application to image compression. IEEE Trans Signal Process 47:1878–1889 Yin Ding and Ivan W. Selesnick. Artifact-free wavelet denoising: non-convex sparse regularization, convex optimization. IEEE Signal Processing Letters, 22(9):1364-1368, September 2015. Ankit Parekh and Ivan W. Selesnick. Convex Fused Lasso Denoising with Non-Convex Regularization and its use for Pulse Detection. IEEE SIGNAL PROCESSING IN MEDICINE AND BIOLOGY SYMPOSIUM, DECEMBER 2015 Khuram Naveed, Muhammad Tahir Akhtar, Muhammad Faisal Siddiqui, Naveedur Rehman. A statistical approach to signal denoising based on data-driven multiscale representation. Digital Signal Processing, Volume 108, January 2021, 102896 Mohamed Belkadi and Abdelhamid Daamouche. Swarm Intelligence Approach to QRS Detection. The International Arab Journal of Information Technology, Vol. 17, No. 4, July 2020. Mohamed Hammad, Mina Ibrahim and Mohiy Hadhoud. A Novel Biometric Based on ECG Signals and Images for Human Authentication. The International Arab Journal of Information Technology, Vol. 13, No. 6A, 2016 Table 1 Table 1. Comparative study in terms of CC, MAE, MSE, SNR and PSNR: results obtained from the computations of the mean of values of MAE, of the mean of seven values of PSNR, of the mean of seven values of CC, the mean of seven values of SNR and the mean of seven values of MSE. Each mean is computed for seven clean ECG signals 103, 105, 106, 107, 109, 112, 113, 115, 116, 117, 119, 121, 124. dat corrupted by Gaussian white noise with different values of 𝑆𝑁𝑅𝑖 before denoising (varying from −5dB to 15dB with the step of 5dB). The Denoising Technique SNRi=-5dB SNRi=0dB SNRi=5dB SNRi=10dB SNRi=15dB The proposed technique MAE: 0.0262 MSE: 0.0014 SNRf (dB): 6.1520 PSNR(dB): 18.4722 CC: 0.8797 MAE: 0.0131 MSE: 3.4167e-04 SNRf (dB): 10.0899 PSNR(dB): 22.4102 CC: 0.9526 MAE: 0.0080 MSE: 1.2500e-04 SNRf (dB): 14.7937 PSNR(dB): 28.1046 CC: 0.9833 MAE: 0.0048 MSE: 4.6583e-05 SNRf (dB): 18.9555 PSNR(dB): 32.9653 CC: 0.9936 MAE: 0.0033 MSE: 2.1455e-05 SNRf (dB): 22.1016 PSNR(dB): 36.2628 CC: 0.9968 WATV based denoising technique [14] MAE: 0.0250 MSE: 0.0011 SNRf (dB): 4.2042 PSNR (dB): 19.2463 CC: 0.8401 MAE: 0.0152 MSE: 0.0014 SNRf (dB): 8.7996 PSNR (dB): 23.4729 CC: 0.9369 MAE: 0.0089 MSE: 1.6154e-04 SNRf (dB): 13.4355 PSNR (dB): 27.6956 CC: 0.9776 MAE: 0.0089 MSE: 5.8455e-05 SNRf (dB): 18.0120 PSNR(dB): 31.8722 CC: 0.9921 MAE: 0.0036 MSE: 2.6167e-05 SNRf (dB): 21.6740 PSNR (dB): 35.9372 CC: 0.9966 Convex fused lasso denoising with non-convex regularization [15] MAE: 0.0218 MSE: 0.0011 SNRf (dB): 6.4122 PSNR (dB): 19.4719 CC: 0.8790 MAE: 0.0115 MSE: 0.0026 SNRf (dB): 10.0130 PSNR (dB): 23.0726 CC: 0.9526 MAE: 0.0097 MSE: 2.1675e-04 SNRf (dB): 13.9230 PSNR(dB): 26.2431 CC: 0.9801 MAE: 0.0275 MSE: 1.0625e-04 SNRf (dB): 17.1456 PSNR(dB): 28.7207 CC: 0.9907 MAE: 0.0038 MSE: 3.5556e-05 SNRf (dB): 21.6516 PSNR (dB): 33.6487 CC: 0.9955 A statistical approach to signal denoising based on data-driven multiscale representation [16] MAE: 0.0232 MSE: 9.1818e-04 SNRf: 6.0243 PSNR (dB): 20.9604 CC: 0.8655 MAE: 0.0118 MSE: 3.1818e-04 SNRf (dB): 9.7688 PSNR (dB): 24.0952 CC: 0.9425 MAE: 0.0083 MSE: 1.4545e-04 SNRf (dB): 13.9352 PSNR (dB): 27.6036 CC: 0.9788 MAE: 0.0048 MSE: 6.1429e-04 SNRf: 17.5690 PSNR (dB) 32.8206 CC: 0.9914 MAE: 0.0034 MSE: 2.1857e-05 SNRf: 20.4362 PSNR (dB): 35.9846 CC: 0.9955 Additional Declarations No competing interests reported. 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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-4540515","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":316691090,"identity":"54ce3de5-cb88-49a6-af74-cd5e83f054e2","order_by":0,"name":"Abdallah Rezgui","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYFAC5jaGBAMbOX72BgZmEB9I4wc8DIxALQVpxpI9ByBaeA4Qo4Xhw+FEgxsJRGqxZz/Y9uCBweEEg5tvDD8XVNgw8EgT0MPDk9hukGCQnid5O8dYesaZNAYevgRCDktsk0gwsC7mu51jIM3bdpjBnoeQX/gfgrQwJzbcPGP8G6SFh6AWCbAtzokTbvCYSROn5cZDkF9AgZxWZs1zJo2HoBb2/uRjD3/8AUXl4c23eSps5AhqQQIcBmBridcAtPABKapHwSgYBaNgBAEAY9s+iWxw1xUAAAAASUVORK5CYII=","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Abdallah","middleName":"","lastName":"Rezgui","suffix":""},{"id":316691091,"identity":"9822da05-83f5-4a31-8d06-4ac55a9d98f6","order_by":1,"name":"Mourad Talbi","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Mourad","middleName":"","lastName":"Talbi","suffix":""}],"badges":[],"createdAt":"2024-06-06 12:57:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4540515/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4540515/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":59916882,"identity":"ce9bd4fe-3047-48ad-b8e1-77ff01254f86","added_by":"auto","created_at":"2024-07-09 09:15:47","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":65456,"visible":true,"origin":"","legend":"\u003cp\u003eThe block diagram of the proposed ECG denoising Technique\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4540515/v1/38fbdbdbc1d629d673434cc6.png"},{"id":59916182,"identity":"7ce456e6-a1cd-4a14-b3bf-3afae9111adb","added_by":"auto","created_at":"2024-07-09 09:07:47","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":32827,"visible":true,"origin":"","legend":"\u003cp\u003eFirst Example of ECG denoising by applying the proposed ECG denoising technique: MSE = 0.000023, MAE= 0.003623, SNRi =19.177929 dB, PSNR = 36.073276 dB, CC= 0.994030.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4540515/v1/2ed7f4ac2523018b0f11a0d3.png"},{"id":59916184,"identity":"3d35fdbc-0ffb-4c24-b73f-3026a9e571e8","added_by":"auto","created_at":"2024-07-09 09:07:47","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":37402,"visible":true,"origin":"","legend":"\u003cp\u003eSecond Example of ECG denoising by applying the proposed ECG denoising technique: MSE = 0.000027, MAE= 0.004042, SNR =19.095152 dB, PSNR = 33.009902dB, CC = 0.993840.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4540515/v1/1812b16d0d18e69de9dd97ec.png"},{"id":59916186,"identity":"43f626e3-d2be-45ee-bcbc-d2182d039575","added_by":"auto","created_at":"2024-07-09 09:07:47","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":35823,"visible":true,"origin":"","legend":"\u003cp\u003eThird Example of ECG denoising by applying the proposed ECG denoising technique: MSE = 0.000178, MAE= 0.009827, SNRi =19.151778 dB, PSNR = 27.196007 dB, CC= 0.993908.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4540515/v1/ec36110971e4b39258918f80.png"},{"id":59916185,"identity":"046b8fe9-02bc-4530-b340-dfadcc12e358","added_by":"auto","created_at":"2024-07-09 09:07:47","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":28347,"visible":true,"origin":"","legend":"\u003cp\u003eFirst Example of ECG denoising by applying the proposed ECG denoising technique: MSE = 0.000012, MAE= 0.002524, SNRi =22.069899 dB, PSNR = 38.965246 dB, CC= 0.996947.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4540515/v1/bb29a2f1821b38a3318592b3.png"},{"id":64060585,"identity":"17b20dec-182a-4ac1-bcc1-443c69e8ddb7","added_by":"auto","created_at":"2024-09-06 00:23:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":641216,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4540515/v1/55e6cc2a-cc1f-401e-97b8-6f39edadbccb.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Novel Electrocardiogram Denoising Method based on Convex fused-Lasso Denoising with Non-Convex Regularization and Wavelet/Total Variation","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIn the literature, there are many methods, such as the entropy, filtering, frequency analysis, time series analysis and models, such as auto regressive, and auto regressive moving average, spectral techniques, like power spectral density, wavelets, thresholding, denoising, Fourier transform, Hilbert\u0026ndash;Huang transform, uncertainty principle, support vector machine, adaptive noise cancellation employed for enhancing the Signal-To-Noise Ratio (SNR) [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Signal denoising was conducted also via the Empirical Mode Decomposition (EMD), which is based on a local and adaptive technique in the frequency-time analysis. Some others are based on statistical model such as the so-called deep learning-based auto-encoder models [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Those models consist in regenerating a clean version of the analyzed signal from a degraded version based on an optimization process of an appropriate objective function. In the same category, Bayesian filters based models such as the extended Kalman filter, the extended Kalman smoother, and the unscented Kalman Filter are also known in bio-signals processing. Fuzzy models are also applied extensively, and also combined with neural networks [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] for signal processing. Also, we can mention the hybrid techniques developed by combining these ones. See Abhijith et al. [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], AlMahamdya and Riley [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] and Babatunde [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], Ben Mabrouk et al. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]; Ho [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]; Mallat [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]; Xia and Suter [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]; Zemni et al. [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Wavelet techniques start primarily by decomposing the signal, deciding the type of thresholding and reconstructing the signal. Actually, wavelets was extended to multi-wavelets, which have shown some performance compared to existing techniques. Techniques based on wavelets/multi-wavelets\u003c/p\u003e \u003cp\u003eincluding the mathematical theory of irregular functions to conduct signal processing, such as the estimation of Lipschitz exponent by means of wavelet/multi-wavelet coefficients or transform [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], performing the singularity detection, and therefore yields signal denoising algorithms employing the singularity detection. A thresholding process are permiting to de-noise the signal, and reconstructing the denoised version by simply applying the inverse multi-wavelet transform [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. In this direction, Geronimo, Hardin and Massopust has introduced a technique for constructing translation and dilation invariant function spaces employing fractal functions defined by a certain class of iterated function systems [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Xia and collaborators (Xia [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]; Xia and Jiang [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]; Xia and Suter [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]) ameliorated such multi-wavelets by constructing a pre-filter design technique dealing with all decomposition steps for the discrete multi-wavelet transform, and appoximating a signal with the lowpass property. In this paper we propose a novel approach of Electrocardiogram (ECG) Denoising based on Wavelet/Total Variation (WATV) and Convex fused lasso Denoising with non-convex regularization. The rest of the paper is organized as follows: in section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, we will deal with our ECG denoising approach, proposed in this work. In section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, we will present results and discussion and finally we will conclude in section \u003cspan refid=\"Sec4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e"},{"header":"2. The proposed ECG denoising technique","content":"\u003cp\u003eIn this paper, we propose a novel approach of Electrocardiogram (ECG) Denoising based on Wavelet/Total Variation (WATV) [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] and Convex fused lasso Denoising with non-convex regularization (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). This approach consists at first step of applying the Discrete Wavelet Transform (DWT) to the noisy ECG signal for obtaining a noisy approximation coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAb}_{1}\\)\u003c/span\u003e\u003c/span\u003e and a noisy details coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cDb}_{1}\\)\u003c/span\u003e\u003c/span\u003e. The latter is denoised by soft thresholding and we obtain a first denoised details coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cDd}_{1}\\)\u003c/span\u003e\u003c/span\u003e. The second step of this approach consists of applying the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(DWT\\)\u003c/span\u003e\u003c/span\u003e to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAb}_{1}\\)\u003c/span\u003e\u003c/span\u003e in order to obtain a second noisy approximation coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAb}_{2}\\)\u003c/span\u003e\u003c/span\u003e and a second noisy details coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cDb}_{2}\\)\u003c/span\u003e\u003c/span\u003e. The latter is denoised by Convex fused lasso denoising with non-convex regularization [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] and we obtain a second denoised details coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cDd}_{2}\\)\u003c/span\u003e\u003c/span\u003e. The noisy approximation coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAb}_{2}\\)\u003c/span\u003e\u003c/span\u003e, is denoised by WATV based denoising technique and we obtain a denoised approximation coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAd}_{2}\\)\u003c/span\u003e\u003c/span\u003e. The inverse of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(DWT\\)\u003c/span\u003e\u003c/span\u003e is then applied to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cDd}_{2}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAd}_{2}\\)\u003c/span\u003e\u003c/span\u003e in order to obtain a denoised approximation coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAd}_{1}\\)\u003c/span\u003e\u003c/span\u003e. The inverse of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(DWT\\)\u003c/span\u003e\u003c/span\u003e is again applied to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cDd}_{1}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAd}_{1}\\)\u003c/span\u003e\u003c/span\u003e for obtaining finally a denoised \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(ECG\\)\u003c/span\u003e\u003c/span\u003e signal. For the soft thresholding of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cDb}_{1}\\)\u003c/span\u003e\u003c/span\u003e, we use a threshold, thr (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), which is expressed as follow:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$thr=\\sigma \\bullet \\sqrt{2\\bullet log\\left(N\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere N is the number of samples of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cDb}_{1}\\)\u003c/span\u003e\u003c/span\u003e and\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\sigma\\)\u003c/span\u003e \u003c/span\u003e is the estimated noise level, and expressed as follow:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\sigma =MAD\\left(\\left|c{D}_{1}\\right|\\right)/0.6745$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThis estimated noise level, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sigma\\)\u003c/span\u003e\u003c/span\u003e, is also used for the application of WATV [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] based denoising technique to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAb}_{2}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e"},{"header":"3. Results and discussion","content":"\u003cp\u003eFor evaluating and testing the performance of our ECG denoising approach, we compared it the WATV based denoising technique [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], the Convex fused lasso denoising with non-convex regularization [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] and a statistical approach to signal denoising based on data-driven multiscale representation [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. This comparison is performed by computing the Signal to Noise Ratio (SNR), the Peak SNR (PSNR), the Mean Square Error (MSE), the Mean Absolute Error (MAE) and the Cross-Correlation (CC), and this for five values of SNR before denoising, SNRi. These values are \u0026minus;\u0026thinsp;5dB, 0dB, 5dB, 10dB and 15dB and the results obtained from the previously mentioned denoising techniques, are listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. According to Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the best results are highlighted in blue color and in cases of SNRi\u0026thinsp;=\u0026thinsp;5dB or SNRi\u0026thinsp;=\u0026thinsp;10dB or SNRi\u0026thinsp;=\u0026thinsp;15dB, they are obtained from the application of the proposed ECG denoising technique.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTherefore, when the SNRi is higher (5dB or 10dB or 15dB), this proposed techni-que outperforms the other previously mentioned techniques used for this evaluation. In Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u0026ndash;5, are illustrated some examples of ECG denoising by applying the proposed technique. According to these figures, the proposed technique permits to cancel the noise while conserving the original signals.\u003c/p\u003e "},{"header":"4. Conclusion","content":"\u003cp\u003eIn this paper, we propose a novel approach of Electrocardiogram (ECG) Denoising based on Wavelet/Total Variation (WATV) and Convex fused lasso Denoising with non-convex regularization. This approach consists at first step of applying the Discrete Wavelet Transform (DWT) to the noisy ECG signal for obtaining a noisy approximation coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAb}_{1}\\)\u003c/span\u003e\u003c/span\u003e and a noisy details coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cDb}_{1}\\)\u003c/span\u003e\u003c/span\u003e. The latter is denoised by soft thresholding and we obtain a first denoised details coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cDd}_{1}\\)\u003c/span\u003e\u003c/span\u003e. The second step of this approach consists of applying the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(DWT\\)\u003c/span\u003e\u003c/span\u003e to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAb}_{1}\\)\u003c/span\u003e\u003c/span\u003e in order to obtain a second noisy approximation coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAb}_{2}\\)\u003c/span\u003e\u003c/span\u003e and a second noisy details coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cDb}_{2}\\)\u003c/span\u003e\u003c/span\u003e. The latter is denoised by Convex fused lasso denoising with non-convex regularization and we obtain a second denoised details coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cDd}_{2}\\)\u003c/span\u003e\u003c/span\u003e. The noisy approximation coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAb}_{2}\\)\u003c/span\u003e\u003c/span\u003e, is denoised by WATV based denoising technique and we obtain a denoised approximation coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAd}_{2}\\)\u003c/span\u003e\u003c/span\u003e. The inverse of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(DWT\\)\u003c/span\u003e\u003c/span\u003e is then applied to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cDd}_{2}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAd}_{2}\\)\u003c/span\u003e\u003c/span\u003e in order to obtain a denoised approximation coefficient, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAd}_{1}\\)\u003c/span\u003e\u003c/span\u003e. The inverse of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(DWT\\)\u003c/span\u003e\u003c/span\u003e is again applied to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cDd}_{1}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({cAd}_{1}\\)\u003c/span\u003e\u003c/span\u003e for obtaining finally a denoised \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(ECG\\)\u003c/span\u003e\u003c/span\u003e signal. The performance of this proposed approach is proved by the computation of the Signal to Noise Ratio (SNR), the Peak SNR (PSNR), the Mean Square Error (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(MSE\\)\u003c/span\u003e\u003c/span\u003e), the Mean Absolute Error (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(MAE\\)\u003c/span\u003e\u003c/span\u003e), and the Cross-Correlation (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(CC\\)\u003c/span\u003e\u003c/span\u003e). In fact, when the SNRi is higher (5dB or 10dB or 15dB), this proposed technique outperforms the other previously mentioned techniques used for this evaluation, WATV based denoising technique, Convex fused lasso denoising with non-convex regularization and A statistical approach to signal denoising based on data-driven multiscale representation.\u003c/p\u003e "},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAbdallah introduce the novel ECG denoising and Mourad Talbi make the different matlab simulations and the two authors wrote the main manuscript text. All authors reviewed the manuscript.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interest declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThere are no Competing Interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding Declaration\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThere was no Funding for this manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eMalika Jallouli, Makerem Zemni, Anouar Ben Mabrouk, Mohamed Ali Mahjoub. Toward new multi-wavelets: associated filters and algorithms. Part I: theoretical framework and investigation of biomedical signals, ECG, and coronavirus cases. Soft Computing (2021) 25:14059\u0026ndash;14079 https://doi.org/10.1007/s00500-021-06217-y \u003c/li\u003e\n\u003cli\u003eAbhijith A, Ruban DP, Rajy X, Mareeta CP (2016) Review of signal processing techniques for detection of power quality events. Am J Eng Appl Sci 9(2):364\u0026ndash;370\u003c/li\u003e\n\u003cli\u003eAlMahamdya M, Riley HB (2014) Performance study of different denoising methods for ECG signals. Procedia Comput Sci 37:325\u0026ndash; 332\u003c/li\u003e\n\u003cli\u003eBabatunde SE (2012) A review of signal processing techniques for heart sound analysis in clinical diagnosis. J Med Eng Technol 36(6):303\u0026ndash;307\u003c/li\u003e\n\u003cli\u003eBen Mabrouk A, Kortas H, Dhifaoui Z (2008a) A wavelet support vector machine coupled method for time series prediction. Int J Wavelets Multiresolution Inf Process 6(6):1\u0026ndash;17\u003c/li\u003e\n\u003cli\u003eHo YF (2002) Singularity detection for regularity scalable image coding. Master thesis, Department of electronic and information engineering, Hong Kong University of Technology\u003c/li\u003e\n\u003cli\u003eMallat S (2008) A wavelet tour of signal processing, 3rd edn. Academic Press, Cambridge\u003c/li\u003e\n\u003cli\u003eXia X-G, Suter BW (1996) Vector-valued wavelets and vector filter banks. IEEE Trans Signal Process 44(3):508\u0026ndash;518\u003c/li\u003e\n\u003cli\u003eZemni M, Jallouli M, Ben Mabrouk A, Mahjoub MA (2019a) Explicit Haar\u0026ndash;Schauder multiwavelet filters, and algorithms. Part II: relative entropy-based estimation for optimal modeling of biomedical signals. Int JWavelets Multiresolution Inf Process 17(05):1950038 \u003c/li\u003e\n\u003cli\u003eZemni M, Jallouli M, Ben Mabrouk A, Mahjoub MA (2019b) ECG signal processing with Haar\u0026ndash;Schauder multiwavelet. In: Proceedings of the 9th international conference on information systems, and technologies\u0026mdash;ICIST. https://doi.org/10.1145/3361570.3361611\u003c/li\u003e\n\u003cli\u003eGeronimo JS, Hardin DP, Massopust PR (1994) Fractal function and wavelet expansions based on several scaling functions. J Approx Theory 78:373\u0026ndash;401\u003c/li\u003e\n\u003cli\u003eXia X-G (1998) A new prefilter design for discrete multiwavelet transforms. IEEE Trans Signal Process 46:1558\u0026ndash;1570\u003c/li\u003e\n\u003cli\u003eXia T, Jiang Q (1999) Optimal multifilter banks: design, related symmetric extension transform, and application to image compression. IEEE Trans Signal Process 47:1878\u0026ndash;1889\u003c/li\u003e\n\u003cli\u003eYin Ding and Ivan W. Selesnick. Artifact-free wavelet denoising: non-convex sparse regularization, convex optimization. IEEE Signal Processing Letters, 22(9):1364-1368, September 2015.\u003c/li\u003e\n\u003cli\u003eAnkit Parekh and Ivan W. Selesnick. Convex Fused Lasso Denoising with Non-Convex Regularization and its use for Pulse Detection. IEEE SIGNAL PROCESSING IN MEDICINE AND BIOLOGY SYMPOSIUM, DECEMBER 2015\u003c/li\u003e\n\u003cli\u003eKhuram Naveed, Muhammad Tahir Akhtar, Muhammad Faisal Siddiqui, Naveedur Rehman. A statistical approach to signal denoising based on data-driven multiscale representation. Digital Signal Processing, Volume 108, January 2021, 102896\u003c/li\u003e\n\u003cli\u003eMohamed Belkadi and Abdelhamid Daamouche. Swarm Intelligence Approach to QRS Detection. The International Arab Journal of Information Technology, Vol. 17, No. 4, July 2020.\u003c/li\u003e\n\u003cli\u003eMohamed Hammad, Mina Ibrahim and Mohiy Hadhoud. A Novel Biometric Based on ECG Signals and Images for Human Authentication. The International Arab Journal of Information Technology, Vol. 13, No. 6A, 2016\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Table 1","content":"\u003cp\u003eTable 1. Comparative study in terms of CC, MAE, MSE, SNR and PSNR: results obtained from the computations of the mean of values of MAE, of the mean of seven values of PSNR, of the mean of seven values of CC, the mean of seven values of SNR and the mean of seven values of MSE. Each mean is computed for seven clean ECG signals 103, 105, 106, 107, 109, 112, 113, 115, 116, 117, 119, 121, 124. dat corrupted by Gaussian white noise with different values of 𝑆𝑁𝑅𝑖 before denoising (varying from \u0026minus;5dB to 15dB with the step of 5dB).\u003c/p\u003e\n\u003ctable style=\"border-collapse:collapse;border:none;\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 88.3pt;border: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;'\u003e\u003cstrong\u003eThe Denoising Technique\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 84.4pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;'\u003e\u003cstrong\u003eSNRi=-5dB\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 88.55pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;'\u003e\u003cstrong\u003eSNRi=0dB\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 88.55pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;'\u003e\u003cstrong\u003eSNRi=5dB\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 74.95pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;'\u003e\u003cstrong\u003eSNRi=10dB\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 90.05pt;border-top: 1pt solid windowtext;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-image: initial;border-left: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;'\u003e\u003cstrong\u003eSNRi=15dB\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 88.3pt;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-left: 1pt solid windowtext;border-image: initial;border-top: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;'\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;'\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;'\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;'\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;'\u003eThe proposed technique\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 84.4pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMAE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.0262\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMSE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.0014\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eSNRf (dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e6.1520\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003ePSNR(dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e18.4722\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eCC:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e0.8797\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 88.55pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMAE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.0131\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMSE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e3.4167e-04\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eSNRf (dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e10.0899\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003ePSNR(dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e22.4102\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eCC:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e0.9526\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 88.55pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMAE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e0.0080\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMSE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e1.2500e-04\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eSNRf (dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e14.7937\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003ePSNR(dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e28.1046\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eCC:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e0.9833\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 74.95pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMAE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e0.0048\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMSE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e4.6583e-05\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eSNRf (dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e18.9555\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003ePSNR(dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e32.9653\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eCC:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e0.9936\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 90.05pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMAE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e0.0033\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMSE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e2.1455e-05\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eSNRf (dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e22.1016\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003ePSNR(dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e36.2628\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eCC:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e0.9968\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 88.3pt;border-right: 1pt solid windowtext;border-bottom: 1pt solid windowtext;border-left: 1pt solid windowtext;border-image: initial;border-top: none;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;'\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;'\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;'\u003eWATV based denoising technique [14]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 84.4pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMAE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.0250\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMSE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e\u003cstrong\u003e\u003cspan style=\"color:#4472C4;\"\u003e0.0011\u003c/span\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eSNRf (dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e4.2042\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003ePSNR (dB): 19.2463\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eCC:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.8401\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 88.55pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMAE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.0152\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMSE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.0014\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eSNRf (dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e8.7996\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003ePSNR (dB): 23.4729\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eCC:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.9369\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 88.55pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMAE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.0089\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMSE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e1.6154e-04\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eSNRf (dB): 13.4355\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003ePSNR (dB): 27.6956\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eCC:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.9776\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 74.95pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMAE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.0089\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMSE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e5.8455e-05\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eSNRf (dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e18.0120\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003ePSNR(dB): 31.8722\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eCC:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.9921\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 90.05pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMAE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.0036\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMSE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e2.6167e-05\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eSNRf (dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New 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90.05pt;border-top: none;border-left: none;border-bottom: 1pt solid windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMAE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.0038\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMSE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e3.5556e-05\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eSNRf (dB):\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e21.6516\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New 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windowtext;border-right: 1pt solid windowtext;padding: 0in 5.4pt;vertical-align: top;\"\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMAE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e0.0034\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eMSE:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e2.1857e-05\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003eSNRf:\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003e20.4362\u003c/p\u003e\n \u003cp style='margin:0in;font-size:13px;font-family:\"Times New Roman\",serif;text-align:center;'\u003ePSNR (dB): 35.9846\u003c/p\u003e\n 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regularization","lastPublishedDoi":"10.21203/rs.3.rs-4540515/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4540515/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we propose a new Electrocardiogram (ECG) denoising approach based on Convex fused lasso Denoising with non-convex regularization and Wavelet/Total Variation (WATV). This approach consists at first step of applying the Discrete Wavelet Transform (DWT) to the noisy ECG signal for obtaining a noisy approximation coefficient, cAb\u003csub\u003e1\u003c/sub\u003e and a noisy details coefficient, cDb\u003csub\u003e1\u003c/sub\u003e. The latter is denoised by soft thresholding and we obtain a denoised details coefficient, cDd\u003csub\u003e1\u003c/sub\u003e. The second step of this approach consists of applying the DWT to cAb\u003csub\u003e1\u003c/sub\u003e in order to obtain a noisy approximation coefficient, cAb\u003csub\u003e2\u003c/sub\u003e and a noisy details coefficient, cDb\u003csub\u003e2\u003c/sub\u003e. The latter is denoised by Convex fused lasso denoising with non-convex regularization and we obtain a denoised details coefficient, cDd\u003csub\u003e2\u003c/sub\u003e. The coefficient, cAb\u003csub\u003e2\u003c/sub\u003e, is denoised by WATV based denoising technique and we obtain a \u0026nbsp;denoised coefficient, cAd\u003csub\u003e2\u003c/sub\u003e. The inverse of DWT is then applied to cDd\u003csub\u003e2\u003c/sub\u003e and cAd\u003csub\u003e2\u003c/sub\u003e in order to obtain a denoised approximation coefficient, cAd\u003csub\u003e1\u003c/sub\u003e. The inverse of DWT is again applied to cDd\u003csub\u003e1\u003c/sub\u003e and cAd\u003csub\u003e1\u003c/sub\u003e for obtaining finally a denoised ECG signal. The performance of this proposed approach is proved by the computation of SNR, the PSNR, the MSE, the Mean Absolute Error (MAE), and the Cross-Correlation (CC).\u003c/p\u003e","manuscriptTitle":"A Novel Electrocardiogram Denoising Method based on Convex fused-Lasso Denoising with Non-Convex Regularization and Wavelet/Total Variation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-09 09:07:42","doi":"10.21203/rs.3.rs-4540515/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":"befe7001-b77e-41ee-96d2-9c73ffcdb262","owner":[],"postedDate":"July 9th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-09-06T00:15:47+00:00","versionOfRecord":[],"versionCreatedAt":"2024-07-09 09:07:42","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4540515","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4540515","identity":"rs-4540515","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}