[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86144-en":3,"doc-seo-86144-105":30,"detail-sidebar-cat-0-en-105":92},{"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},86144,962075114765,"Quinn","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","FlowPET Physics Informed Symplectic Flow Matching for Low Count PET Reconstruction","Low-count Positron Emission Tomography (PET) reconstruction is constrained by dissipative generative models whose phase-space contraction numerically eliminates weak but clinically critical lesion signals. FlowPET proposes a physics-informed solution by reformulating reconstruction as volume-preserving transport in a symplectic phase space. A separable Hamiltonian system parameterization guarantees a divergence-free vector field, while conjugate boundary conditions using Range-Null decomposition enforce data consistency and restrict stochastic injection to unobserved null space. Training via symplectic flow matching and leapfrog inference improves SSIM/PSNR and, most importantly, preserves low-contrast lesions under high noise. Experiments on BrainWeb, clinical pediatric, and UDPET verify robust recovery, with code released publicly.","FlowPET: Physics-Informed Symplectic Flow Matching for Low-Count PET Reconstruction  \nZheng Zhang 1 Hao Tang 1 Yingying Hu 2 Zhanli Hu 3 Jing Qin 1  \narXiv :2607 . 11104v1 [ cs .CV] 13 Jul 2026  \nAbstract  \nLow-count Positron Emission Tomography (PET) reconstruction is severely hindered by the dissipative nature of prevailing generative models, where the inherent phase-space contraction leads to the numerical extinction (“wash-out”) of weak but diagnostically critical lesion signals. To overcome this geometric limitation, we propose FlowPET, a physics-informed framework that reformulates reconstruction as volume-preserving transport ina symplectic phase space. By parameterizing the posterior dynamics via a Separable Hamiltonian System, our approach guarantees a divergencefree vector field by construction, theoretically immunizing weak signals against probability mass collapse. To steer this conservative flow, we introduce conjugate boundary conditions based on the Range-Null space decomposition of the PET operator; this strictly enforces data consistency in the range space while confining stochastic uncertainty injection to the unobserved null space. We train the model via symplectic flow matching and perform inference using a symplectic leapfrog integrator. Extensive experiments on BrainWeb, clinical pediatric, and UDPET datasets demonstrate that FlowPET not only surpasses state-of-the-art deterministic and stochastic baselines in SSIM  \nand PSNR but, more crucially, exhibits superior recovery of low-contrast lesions. The results confirm that imposing Hamiltonian structural constraints offers a robust geometric safeguard for medical inverse problems in high-noise regimes. Code is available at [https://github.com/](https://github.com/)[ ](https://github.com/)xiaochaorouz/FlowPET.  \n1Centre for Smart Health, The Hong Kong Polytechnic University, Hong Kong, China 2Department of Nuclear Medicine, Sun Yat-sen University Cancer Center, Guangzhou, China 3Research Center for Medical AI, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China. Correspondence to: Hao Tang \u003C[howard.haotang@gmail.com](howard.haotang@gmail.com) >.  \nProceedings of the 43 rd International Conference on Machine Learning, Seoul, South Korea. PMLR 306, 2026 . Copyright 2026 by the author(s) .  \nInformation Wash-Out  \nVolumePreserving  \n Noise Signal  \n Weak Lesion Signal  \nSymplectic Transport  \nFigure 1. Conceptual comparison of generative dynamics in PET reconstruction. Standard dissipative solvers induce a contractive field (∇ · v \u003C 0), causing weak lesion signals to be “washed out”alongside noise. In contrast, symplectic solvers lift the dynamics to a symplectic phase space, enforcing volume preservation (∇ · v = 0) to losslessly transport clinically vital signals under strict physical constraints.  \n1. Introduction  \nLow-count Positron Emission Tomography (PET) reconstruction represents a critical frontier in medical imaging, balancing the need for precise metabolic quantification against stringent radiation safety protocols. Reducing tracer dose inevitably degrades the Signal-to-Noise Ratio (SNR) due to Poisson photon-counting statistics. In this regime, thereconstruction task transcends simple inversion; it becomes a complex Bayesian inference problem aiming to recover the posterior distribution conditional on noisy measurements. The paramount challenge is not merely denoising, but the faithful recovery of weak lesion signals, features that are diagnostically vital for early staging yet statistically fragile against the dominant noise floor.  \nTo mitigate the noise amplification inherent in classical algorithms (e.g., OSEM (Hudson & Larkin, 1994)), the field has pivoted to deep learning. While effective, current paradigms face a fundamental dilemma. Deterministic approaches (Zhang et al., 2026 ; 2024 ; Xie et al., 2025 ; Wang & Liu, 2020 ; Cui et al., 2024) minimize reconstruction error by approximating the posterior mea","cbCaifP50tl2CK5G","https://ap.wps.com/l/cbCaifP50tl2CK5G","pdf",10141610,7,1,17,"English","en",105,"# Abstract\n# Introduction\n## Wash-Out in Dissipative Generative Models\n## Motivation for Conservative, Volume-Preserving Sampling\n## FlowPET Framework Overview","[{\"question\":\"What problem does FlowPET target in low-count PET reconstruction?\",\"answer\":\"FlowPET targets the wash-out of weak but diagnostically critical lesion signals caused by the phase-space contraction (negative divergence) of dissipative generative models under low-count noise conditions.\"},{\"question\":\"How does FlowPET prevent weak lesion signals from being extinguished?\",\"answer\":\"FlowPET reformulates posterior sampling as an invertible, volume-preserving evolution in a symplectic phase space, using a separable Hamiltonian dynamics parameterization to construct a divergence-free vector field.\"},{\"question\":\"How does FlowPET maintain data consistency while controlling uncertainty?\",\"answer\":\"FlowPET introduces conjugate boundary conditions based on Range-Null space decomposition, strictly enforcing consistency in the observed range space while confining stochastic uncertainty injection to the unobserved null space.\"}]",1784208886,43,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"flowpet-physics-informed-symplectic-flow-matching-for-low-count-pet-reconstruction","",{"@graph":36,"@context":86},[37,54,69],{"@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":53},"https://docshare.wps.com/document/flowpet-physics-informed-symplectic-flow-matching-for-low-count-pet-reconstruction/86144/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does FlowPET target in low-count PET reconstruction?","Question",{"text":76,"@type":77},"FlowPET targets the wash-out of weak but diagnostically critical lesion signals caused by the phase-space contraction (negative divergence) of dissipative generative models under low-count noise conditions.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does FlowPET prevent weak lesion signals from being extinguished?",{"text":81,"@type":77},"FlowPET reformulates posterior sampling as an invertible, volume-preserving evolution in a symplectic phase space, using a separable Hamiltonian dynamics parameterization to construct a divergence-free vector field.",{"name":83,"@type":74,"acceptedAnswer":84},"How does FlowPET maintain data consistency while controlling uncertainty?",{"text":85,"@type":77},"FlowPET introduces conjugate boundary conditions based on Range-Null space decomposition, strictly enforcing consistency in the observed range space while confining stochastic uncertainty 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