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However, existing approaches primarily focus on spatial domain information, neglecting the periodic information in the frequency domain and the complementary relationship between the two domains. In this paper, we proposed a generative adversarial network that employs a cross-attention mechanism to extract and fuse features across spatial and frequency domains. The method optimizes frequency domain features using spatial domain guidance and refines spatial features with frequency domain information, preserving key details while eliminating redundancy to generate high-quality histological images.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Results<\/jats:title>\n            <jats:p>Our model incorporates a variable-window mixed attention module to dynamically adjust attention window sizes, capturing both local details and global context. A spectral filtering module enhances the extraction of repetitive textures and periodic structures, while a cross-attention fusion module dynamically weights features from both domains, focusing on the most critical information to produce realistic and detailed images.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Conclusions<\/jats:title>\n            <jats:p>The proposed method achieves efficient spatial-frequency domain fusion, significantly improving image generation quality. Experiments on the Patch Camelyon dataset show superior performance over eight state-of-the-art models across five metrics. This approach advances automated histopathological image generation with potential for clinical applications.<\/jats:p>\n          <\/jats:sec>","DOI":"10.1186\/s12859-025-06057-9","type":"journal-article","created":{"date-parts":[[2025,1,27]],"date-time":"2025-01-27T15:10:07Z","timestamp":1737990607000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Hybrid generative adversarial network based on frequency and spatial domain for histopathological image synthesis"],"prefix":"10.1186","volume":"26","author":[{"given":"Qifeng","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chi","family":"Cheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jin","family":"Ma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marzia","family":"Hoque Tania","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,1,27]]},"reference":[{"key":"6057_CR1","doi-asserted-by":"crossref","unstructured":"Al-Sabawy HB, Rahawy AM, Al-Mahmood SS (2021) Standard techniques for formalin-fixed paraffin-embedded tissue: a pathologist's perspective","DOI":"10.33899\/ijvs.2021.131918.2023"},{"issue":"4","key":"6057_CR2","doi-asserted-by":"publisher","first-page":"1208","DOI":"10.1017\/S1431927614001329","volume":"20","author":"J Buytaert","year":"2014","unstructured":"Buytaert J, Goyens J, De Greef D, Aerts P, Dirckx J. 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