Frequency domain characteristics and optimization of image generation for GANs

Frequency domain characteristics and optimization of image generation for GANs | 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 Frequency domain characteristics and optimization of image generation for GANs Xueyi Ye, Mingcong Sui, Maosheng Zeng, Zhuo Han, Hao Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4537002/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 13 You are reading this latest preprint version Abstract In recent years, Generative Adversarial Networks (GANs) have demonstrated enormous promise in areas connected to image generation. As the model generation performance continues to improve and the generated images become more realistic, it is difficult to effectively distinguish between the real image and the generated image. Therefore, the problem of discriminating and optimizing the generated images (adversarial discrimination) has become necessary, and subsequent optimization plans are proposed based on the discrimination strategy. However, due to the nature of convolution, the two-dimensional power spectrum curve of the generated image is low overall; that is, compared with the real image, there is energy loss at each frequency (without other processing), and the curve drops rapidly and approaches zero, which is obviously different from the real image. In particular, the curve of the image generated by transposed convolution has a clear upward trend at the very high-frequency part, which is contrary to the characteristic of the real image, which is that the energy decreases with increasing frequency. Based on the discussion of the characteristics and inducements of the two-dimensional power spectrum curve of the generated image, we present a discrimination approach based on curve warping at high frequency and energy loss to improve the discrimination capacity of the generated image and realize the effective discrimination between the real image and the generated image. Based on this, we present the power spectrum loss function to improve the upward warping characteristics of the very high-frequency part of the two-dimensional power spectrum curve without degrading the quality of the generated image and the high-frequency feature loss function to improve the quality of the generated image. The value and efficiency of the proposed discrimination approach in this study are demonstrated on multiple GANs models, including WGAN, WGAN-GP, and SAGAN, with the dataset celeba, and the GANs model with encoder-decoder as the generator with the dataset CelebA-HQ. The two loss functions proposed are also demonstrated on multiple GANs models, including WGAN, WGAN-GP, and SAGAN with the dataset FFHQ. After adding the high-frequency feature loss, the FID decreases by 5.97, 5.15, and 6.56, respectively. After adding the power spectrum loss, the above models can improve the upward warping characteristics of the two-dimensional power spectrum curve in the very high-frequency part of the generated image to a certain extent. The FID decreases by 17.4, 11.55 and 12.27 when the weight is fixed, and 12.66, 8.15 and 4.46 when the weight is variable, respectively. Generative adversarial network (GANs) Frequency domain characteristics Dis-crimination method Power spectrum loss High frequency feature loss Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Full Text Additional Declarations No competing interests reported. Supplementary Files Table1.jpg table2.jpg Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 19 Aug, 2025 Reviews received at journal 17 Aug, 2025 Reviews received at journal 16 Aug, 2025 Reviewers agreed at journal 04 Aug, 2025 Reviewers agreed at journal 02 Aug, 2025 Reviewers agreed at journal 01 Aug, 2025 Reviewers agreed at journal 30 Jul, 2025 Reviews received at journal 30 Jul, 2025 Reviewers agreed at journal 30 Jul, 2025 Reviewers invited by journal 30 Jul, 2025 Editor assigned by journal 07 Jun, 2024 Submission checks completed at journal 07 Jun, 2024 First submitted to journal 05 Jun, 2024 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-4537002","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":314804878,"identity":"8b42dae3-f797-41b3-bfed-a99b2b90d737","order_by":0,"name":"Xueyi 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GANs","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-journal-of-supercomputing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [The Journal of Supercomputing](https://www.springer.com/journal/11227)","snPcode":"11227","submissionUrl":"https://submission.nature.com/new-submission/11227/3","title":"The Journal of Supercomputing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer 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As the model generation performance continues to improve and the generated images become more realistic, it is difficult to effectively distinguish between the real image and the generated image. Therefore, the problem of discriminating and optimizing the generated images (adversarial discrimination) has become necessary, and subsequent optimization plans are proposed based on the discrimination strategy. However, due to the nature of convolution, the two-dimensional power spectrum curve of the generated image is low overall; that is, compared with the real image, there is energy loss at each frequency (without other processing), and the curve drops rapidly and approaches zero, which is obviously different from the real image. In particular, the curve of the image generated by transposed convolution has a clear upward trend at the very high-frequency part, which is contrary to the characteristic of the real image, which is that the energy decreases with increasing frequency. Based on the discussion of the characteristics and inducements of the two-dimensional power spectrum curve of the generated image, we present a discrimination approach based on curve warping at high frequency and energy loss to improve the discrimination capacity of the generated image and realize the effective discrimination between the real image and the generated image. Based on this, we present the power spectrum loss function to improve the upward warping characteristics of the very high-frequency part of the two-dimensional power spectrum curve without degrading the quality of the generated image and the high-frequency feature loss function to improve the quality of the generated image. The value and efficiency of the proposed discrimination approach in this study are demonstrated on multiple GANs models, including WGAN, WGAN-GP, and SAGAN, with the dataset celeba, and the GANs model with encoder-decoder as the generator with the dataset CelebA-HQ. The two loss functions proposed are also demonstrated on multiple GANs models, including WGAN, WGAN-GP, and SAGAN with the dataset FFHQ. After adding the high-frequency feature loss, the FID decreases by 5.97, 5.15, and 6.56, respectively. After adding the power spectrum loss, the above models can improve the upward warping characteristics of the two-dimensional power spectrum curve in the very high-frequency part of the generated image to a certain extent. The FID decreases by 17.4, 11.55 and 12.27 when the weight is fixed, and 12.66, 8.15 and 4.46 when the weight is variable, respectively.\u003c/p\u003e","manuscriptTitle":"Frequency domain characteristics and optimization of image generation for GANs","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-28 15:59:14","doi":"10.21203/rs.3.rs-4537002/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-08-19T15:50:16+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-17T10:07:57+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-08-17T03:59:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"62640280614674676220125418156223926258","date":"2025-08-04T19:11:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"212646181309482236893873668720985159970","date":"2025-08-02T10:08:16+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"214926044728636327158966750184660563839","date":"2025-08-01T13:34:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"11319147104701239583563007671333990583","date":"2025-07-31T00:07:42+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-30T14:42:34+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"233285258802712180928252694782180184335","date":"2025-07-30T14:25:15+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-07-30T13:03:07+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-06-07T12:45:10+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-06-07T12:43:53+00:00","index":"","fulltext":""},{"type":"submitted","content":"The Journal of Supercomputing","date":"2024-06-06T03:21:13+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-journal-of-supercomputing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [The Journal of Supercomputing](https://www.springer.com/journal/11227)","snPcode":"11227","submissionUrl":"https://submission.nature.com/new-submission/11227/3","title":"The Journal of Supercomputing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"46b6624b-7c41-4521-a83f-e71822005b8f","owner":[],"postedDate":"June 28th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-11-21T01:08:18+00:00","versionOfRecord":[],"versionCreatedAt":"2024-06-28 15:59:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4537002","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4537002","identity":"rs-4537002","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}