[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86272-en":3,"doc-seo-86272-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86272,1099514068365,"Aurelia","https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068",8,"Research & Report","GB-SVFBP: Gaussian-Based Shift-Variant FBP Neural Network","GB-SVFBP introduces a Gaussian-Based Shift-Variant FBP neural network to improve differentiable shift-variant filtered backprojection. The method addresses limitations of trajectory-specific filter design in differentiable SVFBP by learning trajectory-related components within a physics-based pipeline. Prior PCA compression reduces parameters but is restricted by linear constraints on compressibility. GB-SVFBP replaces the redundancy weights with a trainable 2D Gaussian mixture model, achieving about a 99% reduction in trainable parameters while maintaining high reconstruction quality with minimal accuracy trade-off.","GB-SVFBP: Gaussian-Based Shift-Variant FBP neural network  \nChengze Ye, Linda-Sophie Schneider, Yipeng Sun, and Andreas Maier  \nPattern Recognition Lab, Friedrich-Alexander University Erlangen-Nuremberg, Erlangen, Germany  \nmarkedly enhancing reconstruction efficiency. However, it should be noted that the shift-variant FBP algorithm has its own limitations. Specifically, for each unique trajectory, a dedicated filtering component must be carefully designed, which becomes increasingly complex and challenging as the scanning paths deviate further from simple geometries. In order to address this issue, Ye et al. [3, 4] proposed a differentiable shift-variant FBP model based on known operator learning [5], which integrates data-driven approaches with the conventional physics-based reconstruction process. This model maps the shift-variant FBP algorithm into a neural network framework, thereby enabling data-driven estimation of the trajectory-related components in the filtering process. This approach eliminates the necessity for manually designing filters for each trajectory, thereby significantly enhancing the flexibility and adaptability of the reconstruction algorithm. However, the model’s parameter count becomes exceedingly large due to the necessity of estimating a unique weight for each projection during the filtering process.  \nYe et al. [6] demonstrates that the trained parameters in the neural network exhibit significant redundancy and compressibility when subjected to principal component analysis (PCA) . By decomposing these weights into a trainable eigenvector matrix, compressed weights, and a mean vector, the method effectively compresses the network parameters, achieving a reduction of nearly 80% . However, the linear transformation used in this approach imposes inherent constraints on the compression capability.  \nIn order to address these constraints, a Gaussian-Based ShiftVariant FBP (GB-SVFBP) model is proposed. This network extends the differentiable FBP framework by introducing a trainable two-dimensional (2D) Gaussian Mixture Model (GMM) to represent trajectory-related components in the filtering process. This design significantly reduces the number of trainable parameters while preserving high reconstruction quality. Specifically, our approach achieves a substantial 99% reduction in the number of trainable parameters compared to traditional differentiable shift-variant FBP models, accompanied by a minimal accuracy trade-off.  \n2 Materials and Methods  \n2.1 Differentiable Shift-Variant FBP Model  \nThe neural network adaptation of the shift-variant filtered backprojection (FBP) method [2] introduces a data-driven framework for reconstruction that extends the traditional algorithm with modern machine learning techniques.  \nThis paradigm represents a significant development in the field by reformulating the conventional shift-variant FBP algorithm into a fully differentiable framework. This transformation is achieved by leveraging principles of known operator learning. A key advantage of this approach is its capacity to optimize the trajectory-related part during filtering through backpropagation, tailored to the specific trajectory geometry of the imaging system. This mechanism has been shown to enhance the flexibility and reconstruction efficiency of the method.  \nThe shift-variant FBP algorithm is reformulated into a neural network-compatible representation. This results in the following equation [3, 4]:  \nx = AT3dwdAT2dDwredwsinoDA2dwcosp (1)  \nIn this pipeline, the reconstruction process operates on conebeam projection data p through a sequence of mathematical operations. These operations include weight applications (wcos , wsino , wred , wd), differentiation (D), the 2D Radon transform (A2d), 2D backprojection (AT2d), and finally, thereconstruction of the volume via 3D backprojection (AT3d) . Among these, wred represents trajectory-dependent weightsand is the only layer in the reconstruction pipeline that cont","cbCailQkgqro0MFT","https://ap.wps.com/l/cbCailQkgqro0MFT","pdf",1022302,5,1,4,"English","en",105,"# GB-SVFBP: Gaussian-Based Shift-Variant FBP Neural Network\n## Differentiable Shift-Variant FBP Model\n## PCA-Based Shift-Variant FBP Model","[{\"question\":\"What problem does the differentiable shift-variant FBP framework aim to solve?\",\"answer\":\"It reformulates the shift-variant FBP algorithm into a fully differentiable, operator-learning-based network, enabling trajectory-dependent optimization of filtering components via backpropagation and improving reconstruction flexibility and efficiency.\"},{\"question\":\"How does PCA-based compression reduce parameters in shift-variant FBP?\",\"answer\":\"It decomposes the trajectory-related redundancy weights into a trainable eigenvector matrix, compressed low-dimensional weights, and a mean vector, then reconstructs the high-dimensional weights for use in the reconstruction pipeline, achieving nearly 80% reduction.\"},{\"question\":\"What is new in GB-SVFBP compared with the PCA-based approach?\",\"answer\":\"GB-SVFBP introduces a trainable 2D Gaussian Mixture Model to represent trajectory-related components in the filtering stage, significantly reducing trainable parameters (about 99%) while preserving reconstruction quality with only a minimal accuracy trade-off.\"}]",1784209957,10,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"gb-svfbp-gaussian-based-shift-variant-fbp-neural-network","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":22},"https://docshare.wps.com/document/gb-svfbp-gaussian-based-shift-variant-fbp-neural-network/86272/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the differentiable shift-variant FBP framework aim to solve?","Question",{"text":75,"@type":76},"It reformulates the shift-variant FBP algorithm into a fully differentiable, operator-learning-based network, enabling trajectory-dependent optimization of filtering components via backpropagation and improving reconstruction flexibility and efficiency.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does PCA-based compression reduce parameters in shift-variant FBP?",{"text":80,"@type":76},"It decomposes the trajectory-related redundancy weights into a trainable eigenvector matrix, compressed low-dimensional weights, and a mean vector, then reconstructs the high-dimensional weights for use in the reconstruction pipeline, achieving nearly 80% reduction.",{"name":82,"@type":73,"acceptedAnswer":83},"What is new in GB-SVFBP compared with the PCA-based approach?",{"text":84,"@type":76},"GB-SVFBP introduces a trainable 2D Gaussian Mixture Model to represent trajectory-related components in the filtering stage, significantly reducing trainable parameters (about 99%) while preserving reconstruction quality with only a minimal accuracy trade-off.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,109,114,119,122,127,130,133],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & 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