Mahmoud\u00a0Nasr<\/a>,\u00a0Adam\u00a0Pi\u00f3rkowski,\u00a0Krzysztof\u00a0Brzostowski,\u00a0Fathi E. Abd\u00a0El-Samie\u00a0<\/p>\n\n\n\nKeywords<\/strong>: Quaternion, Bilateral filter, Reconstruction kernels, Denoising, SSIM, PSNR, Image quality metrics<\/p>\n\n\n\n<\/p>\n","protected":false},"excerpt":{"rendered":"
Removing noise from reconstructed Computed Tomography (CT) images without raw projection data poses a major challenge in medical imaging, especially with sharp or medium reconstruction kernels that introduce high-frequency noise. This paper presents a novel technique combining quaternion mathematics and bilateral filtering to address this. The proposed Quaternion Bilateral Filter (QBF) preserves vital anatomical structures […]<\/p>\n","protected":false},"featured_media":0,"template":"","research_type":[8],"research_team":[15],"class_list":["post-29370","research","type-research","status-publish","hentry","research_type-publications","research_team-computational-neuroscience"],"yoast_head":"\n
A novel approach for CT image smoothing: Quaternion Bilateral Filtering for kernel conversion - Centre for Computational Personalized Medicine<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sano.science\/research\/29370\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A novel approach for CT image smoothing: Quaternion Bilateral Filtering for kernel conversion\" \/>\n<meta property=\"og:description\" content=\"Removing noise from reconstructed Computed Tomography (CT) images without raw projection data poses a major challenge in medical imaging, especially with sharp or medium reconstruction kernels that introduce high-frequency noise. This paper presents a novel technique combining quaternion mathematics and bilateral filtering to address this. The proposed Quaternion Bilateral Filter (QBF) preserves vital anatomical structures […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sano.science\/research\/29370\/\" \/>\n<meta property=\"og:site_name\" content=\"Centre for Computational Personalized Medicine\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/sano.science\/\" \/>\n<meta property=\"article:modified_time\" content=\"2026-02-24T15:15:05+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@sanoscience\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/sano.science\\\/research\\\/29370\\\/\",\"url\":\"https:\\\/\\\/sano.science\\\/research\\\/29370\\\/\",\"name\":\"A novel approach for CT image smoothing: Quaternion Bilateral Filtering for kernel conversion - Centre for Computational Personalized Medicine\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/sano.science\\\/#website\"},\"datePublished\":\"2026-02-24T15:14:20+00:00\",\"dateModified\":\"2026-02-24T15:15:05+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/sano.science\\\/research\\\/29370\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/sano.science\\\/research\\\/29370\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/sano.science\\\/research\\\/29370\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/sano.science\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Research\",\"item\":\"https:\\\/\\\/sano.science\\\/research\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Publications\",\"item\":\"https:\\\/\\\/sano.science\\\/research-type\\\/publications\\\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"A novel approach for CT image smoothing: Quaternion Bilateral Filtering for kernel conversion\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/sano.science\\\/#website\",\"url\":\"https:\\\/\\\/sano.science\\\/\",\"name\":\"Centre for Computational Personalized Medicine\",\"description\":\"Sano \u2013 Centre for Computational Medicine\",\"publisher\":{\"@id\":\"https:\\\/\\\/sano.science\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/sano.science\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/sano.science\\\/#organization\",\"name\":\"Sano \u2013 Centre for Computational Medicine\",\"alternateName\":\"Sano\",\"url\":\"https:\\\/\\\/sano.science\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/sano.science\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/sano.science\\\/wp-content\\\/uploads\\\/2024\\\/05\\\/logo_sano_podstawowe.png\",\"contentUrl\":\"https:\\\/\\\/sano.science\\\/wp-content\\\/uploads\\\/2024\\\/05\\\/logo_sano_podstawowe.png\",\"width\":700,\"height\":265,\"caption\":\"Sano \u2013 Centre for Computational Medicine\"},\"image\":{\"@id\":\"https:\\\/\\\/sano.science\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/sano.science\\\/\",\"https:\\\/\\\/x.com\\\/sanoscience\",\"https:\\\/\\\/www.linkedin.com\\\/company\\\/sanoscience\\\/\",\"https:\\\/\\\/www.youtube.com\\\/channel\\\/UCDZ_8TcjMWUG2ZcgKKgfpwQ\",\"https:\\\/\\\/bsky.app\\\/profile\\\/sanoscience.bsky.social\"]}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A novel approach for CT image smoothing: Quaternion Bilateral Filtering for kernel conversion - Centre for Computational Personalized Medicine","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/sano.science\/research\/29370\/","og_locale":"en_US","og_type":"article","og_title":"A novel approach for CT image smoothing: Quaternion Bilateral Filtering for kernel conversion","og_description":"Removing noise from reconstructed Computed Tomography (CT) images without raw projection data poses a major challenge in medical imaging, especially with sharp or medium reconstruction kernels that introduce high-frequency noise. This paper presents a novel technique combining quaternion mathematics and bilateral filtering to address this. The proposed Quaternion Bilateral Filter (QBF) preserves vital anatomical structures […]","og_url":"https:\/\/sano.science\/research\/29370\/","og_site_name":"Centre for Computational Personalized Medicine","article_publisher":"https:\/\/www.facebook.com\/sano.science\/","article_modified_time":"2026-02-24T15:15:05+00:00","twitter_card":"summary_large_image","twitter_site":"@sanoscience","twitter_misc":{"Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/sano.science\/research\/29370\/","url":"https:\/\/sano.science\/research\/29370\/","name":"A novel approach for CT image smoothing: Quaternion Bilateral Filtering for kernel conversion - Centre for Computational Personalized Medicine","isPartOf":{"@id":"https:\/\/sano.science\/#website"},"datePublished":"2026-02-24T15:14:20+00:00","dateModified":"2026-02-24T15:15:05+00:00","breadcrumb":{"@id":"https:\/\/sano.science\/research\/29370\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/sano.science\/research\/29370\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/sano.science\/research\/29370\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/sano.science\/"},{"@type":"ListItem","position":2,"name":"Research","item":"https:\/\/sano.science\/research\/"},{"@type":"ListItem","position":3,"name":"Publications","item":"https:\/\/sano.science\/research-type\/publications\/"},{"@type":"ListItem","position":4,"name":"A novel approach for CT image smoothing: Quaternion Bilateral Filtering for kernel conversion"}]},{"@type":"WebSite","@id":"https:\/\/sano.science\/#website","url":"https:\/\/sano.science\/","name":"Centre for Computational Personalized Medicine","description":"Sano \u2013 Centre for Computational Medicine","publisher":{"@id":"https:\/\/sano.science\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/sano.science\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/sano.science\/#organization","name":"Sano \u2013 Centre for Computational Medicine","alternateName":"Sano","url":"https:\/\/sano.science\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/sano.science\/#\/schema\/logo\/image\/","url":"https:\/\/sano.science\/wp-content\/uploads\/2024\/05\/logo_sano_podstawowe.png","contentUrl":"https:\/\/sano.science\/wp-content\/uploads\/2024\/05\/logo_sano_podstawowe.png","width":700,"height":265,"caption":"Sano \u2013 Centre for Computational Medicine"},"image":{"@id":"https:\/\/sano.science\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/sano.science\/","https:\/\/x.com\/sanoscience","https:\/\/www.linkedin.com\/company\/sanoscience\/","https:\/\/www.youtube.com\/channel\/UCDZ_8TcjMWUG2ZcgKKgfpwQ","https:\/\/bsky.app\/profile\/sanoscience.bsky.social"]}]}},"acf":[],"gutenberg_blocks":[{"blockName":"custom-styles","attrs":{"styles":""}},{"blockName":"core\/paragraph","attrs":{"epAnimationGeneratedClass":"edplus_anim-m12gky","epGeneratedClass":"eplus-wrapper"},"innerBlocks":[],"innerHTML":"\n<p class=\" eplus-wrapper\">Removing noise from reconstructed Computed Tomography (CT) images without raw projection data poses a major challenge in medical imaging, especially with sharp or medium reconstruction kernels that introduce high-frequency noise. This paper presents a novel technique combining quaternion mathematics and bilateral filtering to address this. The proposed Quaternion Bilateral Filter (QBF) preserves vital anatomical structures while reducing kernel-induced noise by representing CT scans in quaternion format, jointly encoding RGB channels. Unlike traditional methods relying on raw data or grayscale filtering, our approach operates directly on sharp-kernel reconstructed images, transforming them to match the quality of soft-kernel outputs (e.g., B30f) using paired patient data. QBF\u2019s performance is validated through full-reference metrics (SSIM, PSNR, MAE, RMSE) and no-reference perceptual measures (NIQE, BRISQUE, PIQE). Results demonstrate QBF\u2019s superiority over conventional Bilateral Filter (BF), Non-Local Means (NLM), wavelet, and CNN-based methods, with SSIM of 0.96 and PSNR of 36.3 on B50f reconstructions. Segmentation-based visual assessment confirms that QBF-preserved images retain essential structural details for downstream diagnostics. The study highlights quaternion filtering as a lightweight, interpretable, and efficient alternative to deep learning for post-reconstruction CT enhancement.<\/p>\n","innerContent":["\n<p class=\" eplus-wrapper\">Removing noise from reconstructed Computed Tomography (CT) images without raw projection data poses a major challenge in medical imaging, especially with sharp or medium reconstruction kernels that introduce high-frequency noise. This paper presents a novel technique combining quaternion mathematics and bilateral filtering to address this. The proposed Quaternion Bilateral Filter (QBF) preserves vital anatomical structures while reducing kernel-induced noise by representing CT scans in quaternion format, jointly encoding RGB channels. Unlike traditional methods relying on raw data or grayscale filtering, our approach operates directly on sharp-kernel reconstructed images, transforming them to match the quality of soft-kernel outputs (e.g., B30f) using paired patient data. QBF\u2019s performance is validated through full-reference metrics (SSIM, PSNR, MAE, RMSE) and no-reference perceptual measures (NIQE, BRISQUE, PIQE). Results demonstrate QBF\u2019s superiority over conventional Bilateral Filter (BF), Non-Local Means (NLM), wavelet, and CNN-based methods, with SSIM of 0.96 and PSNR of 36.3 on B50f reconstructions. Segmentation-based visual assessment confirms that QBF-preserved images retain essential structural details for downstream diagnostics. The study highlights quaternion filtering as a lightweight, interpretable, and efficient alternative to deep learning for post-reconstruction CT enhancement.<\/p>\n"]},{"blockName":"core\/spacer","attrs":{"height":"50px","epAnimationGeneratedClass":"edplus_anim-gBB12B","epGeneratedClass":"eplus-wrapper"},"innerBlocks":[],"innerHTML":"\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer eplus-wrapper\"><\/div>\n","innerContent":["\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer eplus-wrapper\"><\/div>\n"]},{"blockName":"acf\/button","attrs":{"title":"","button_type":"link","url":"","button_style":"primary","target":"_self","button_extra_classes":""},"innerBlocks":[],"innerHTML":"","innerContent":[]},{"blockName":"core\/spacer","attrs":{"height":"50px","epAnimationGeneratedClass":"edplus_anim-gBB12B","epGeneratedClass":"eplus-wrapper"},"innerBlocks":[],"innerHTML":"\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer eplus-wrapper\"><\/div>\n","innerContent":["\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer eplus-wrapper\"><\/div>\n"]},{"blockName":"core\/paragraph","attrs":{"epAnimationGeneratedClass":"edplus_anim-8A9p1a","epGeneratedClass":"eplus-wrapper"},"innerBlocks":[],"innerHTML":"\n<p class=\" eplus-wrapper\"><strong>Autors<\/strong>: <a href=\"https:\/\/sano.science\/people\/mahmoud-nasr\/\" type=\"people\" id=\"14244\">Mahmoud\u00a0Nasr<\/a>,\u00a0Adam\u00a0Pi\u00f3rkowski,\u00a0Krzysztof\u00a0Brzostowski,\u00a0Fathi E. Abd\u00a0El-Samie\u00a0<\/p>\n","innerContent":["\n<p class=\" eplus-wrapper\"><strong>Autors<\/strong>: <a href=\"https:\/\/sano.science\/people\/mahmoud-nasr\/\" type=\"people\" id=\"14244\">Mahmoud\u00a0Nasr<\/a>,\u00a0Adam\u00a0Pi\u00f3rkowski,\u00a0Krzysztof\u00a0Brzostowski,\u00a0Fathi E. Abd\u00a0El-Samie\u00a0<\/p>\n"]},{"blockName":"core\/paragraph","attrs":{"epAnimationGeneratedClass":"edplus_anim-8A9p1a","epGeneratedClass":"eplus-wrapper"},"innerBlocks":[],"innerHTML":"\n<p class=\" eplus-wrapper\"><strong>Keywords<\/strong>: Quaternion, Bilateral filter, Reconstruction kernels, Denoising, SSIM, PSNR, Image quality metrics<\/p>\n","innerContent":["\n<p class=\" eplus-wrapper\"><strong>Keywords<\/strong>: Quaternion, Bilateral filter, Reconstruction kernels, Denoising, SSIM, PSNR, Image quality metrics<\/p>\n"]},{"blockName":"core\/paragraph","attrs":{"epAnimationGeneratedClass":"edplus_anim-zf4hLa","epGeneratedClass":"eplus-wrapper"},"innerBlocks":[],"innerHTML":"\n<p class=\" eplus-wrapper\"><\/p>\n","innerContent":["\n<p class=\" eplus-wrapper\"><\/p>\n"]}],"meta_data":{"is_automatically_other_posts":true,"number_of_posts":"3","is_automatically_check_also_posts":true},"_links":{"self":[{"href":"https:\/\/sano.science\/index.php\/wp-json\/wp\/v2\/research\/29370","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sano.science\/index.php\/wp-json\/wp\/v2\/research"}],"about":[{"href":"https:\/\/sano.science\/index.php\/wp-json\/wp\/v2\/types\/research"}],"version-history":[{"count":7,"href":"https:\/\/sano.science\/index.php\/wp-json\/wp\/v2\/research\/29370\/revisions"}],"predecessor-version":[{"id":29377,"href":"https:\/\/sano.science\/index.php\/wp-json\/wp\/v2\/research\/29370\/revisions\/29377"}],"wp:attachment":[{"href":"https:\/\/sano.science\/index.php\/wp-json\/wp\/v2\/media?parent=29370"}],"wp:term":[{"taxonomy":"research_type","embeddable":true,"href":"https:\/\/sano.science\/index.php\/wp-json\/wp\/v2\/research_type?post=29370"},{"taxonomy":"research_team","embeddable":true,"href":"https:\/\/sano.science\/index.php\/wp-json\/wp\/v2\/research_team?post=29370"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}