FlowPET: Physics-Informed Symplectic Flow Matching for Low-Count PET Reconstruction

• URL: http://arxiv.org/abs/2607.11104v1
• Date: Mon, 13 Jul 2026 05:26:15 GMT
• Title: FlowPET: Physics-Informed Symplectic Flow Matching for Low-Count PET Reconstruction
• Abstract summary: Low-count Positron Emission Tomography (PET) reconstruction is severely hindered by the dissipative nature of prevailing generative models.<n>We propose textbfFlowPET, a physics-informed framework that reformulates reconstruction as volume-preserving transport in a symplectic phase space.<n>Our approach guarantees a divergence-free vector field by construction, theoretically immunizing weak signals against probability mass collapse.
• Score: 21.5716184040742
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Low-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 \textbf{FlowPET}, a physics-informed framework that reformulates reconstruction as volume-preserving transport in a symplectic phase space. By parameterizing the posterior dynamics via a Separable Hamiltonian System, our approach guarantees a divergence-free 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 \textbf{FlowPET} not only surpasses state-of-the-art deterministic and stochastic baselines in SSIM and 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.

Related papers

• Null-Space Diffusion Restoration with Adaptive Uncertainty-Guided Fusion for Ultrasound Speckle Reduction [2.081691729410268]
  Ultrasound B-mode imaging commonly suffers from speckle noise and artifacts.<n>New uncertainty-guided null-space diffusion (UGNS) framework enforces consistency correction on a stabilized positive-envelope proxy.<n>It is successfully validated that UGNS effectively suppresses speckle noise while preserving fine spatial resolution.
  arXiv  Detail & Related papers  (2026-08-30T14:45:13Z)
• Test-time Adaptation of Pelvic Bone Segmentation Models via Dynamic Reliability-Guided [62.10276009853225]
  Reliable pelvic bone segmentation from CT is essential for robot-assisted pelvic trauma surgery.<n>Existing methods show limited effectiveness for PBS.<n>We propose a novel closed-loop dynamic Reliability-Guided framework (ReGA) for PBS.
  arXiv  Detail & Related papers  (2026-08-01T08:13:20Z)
• Semi-Supervised Conditional Generative Learning through Stochastic Interpolation and Sufficient Representations [12.299177496689621]
  We propose a semi-supervised framework combining conditional intrinsic with low-dimensional latent representations.<n>RepG decomposes generation into two stages: label-dependent latent sampling and high-dimensional reconstruction.
  arXiv  Detail & Related papers  (2026-07-18T09:21:53Z)
• Delta-Diffusion: Modeling Longitudinal Brain Amyloid-PET Trajectories via Conditional Poisson Diffusion Bridge [2.4844989305098997]
  We propose Delta-Diffusion, a novel progression-aware framework that redefines longitudinal PET synthesis as a conditional Poisson Diffusion Bridge (PDB) process.<n>Delta-Diffusion demonstrates superior performance in capturing variations in amyloid deposition compared to state-of-the-art methods.
  arXiv  Detail & Related papers  (2026-06-20T20:34:48Z)
• Structure-Preserving Neural Surrogates with Tractable Uncertainty Quantification [5.8001568807112855]
  Recent advances in machine learning provide a means of near-real-time solution to partial differential equations (PDEs)<n>We construct data-driven reduced-order models that serve as structure-preserving, real-time surrogates.
  arXiv  Detail & Related papers  (2026-06-10T04:27:23Z)
• Next-Acceleration-Scale Prediction for Autoregressive MRI Reconstruction [52.32112533846212]
  MRI reconstruction is an inherently ill-posed inverse problem, since incomplete measurements admit many plausible solutions.<n>We address this limitation by moving reconstruction to discrete multi-scale latent space and posing it as autoregressive next-acceleration-scale prediction.<n>We show that our approach delivers improved reconstruction performance across diverse sampling patterns under extreme undersampling.
  arXiv  Detail & Related papers  (2026-05-19T04:40:50Z)
• SCALE:Scalable Conditional Atlas-Level Endpoint transport for virtual cell perturbation prediction [46.645872209565574]
  We present a specialized large-scale foundation model for virtual cell perturbation prediction.<n>First, we build a BioNeMo-based training and inference framework that substantially improves data throughput.<n>Second, we formulate perturbation prediction as conditional transport and implement it with a set-aware flow architecture.<n>Third, we evaluate the model on Tahoe-100M using a rigorous cell-level protocol centered on biologically meaningful metrics.
  arXiv  Detail & Related papers  (2026-03-18T05:51:08Z)
• CT-Conditioned Diffusion Prior with Physics-Constrained Sampling for PET Super-Resolution [25.790321547743066]
  We formulate PET super-resolution as posterior inference under heterogeneous system configurations.<n>We propose a CT-conditioned diffusion framework with physics-constrained sampling.<n>Under both standard and OOD settings, the proposed method consistently improves experimental metrics and lesion-level clinical relevance indicators.
  arXiv  Detail & Related papers  (2026-03-14T11:28:23Z)
• Spinverse: Differentiable Physics for Permeability-Aware Microstructure Reconstruction from Diffusion MRI [1.6863755729554886]
  We present Spinverse, a permeability-aware reconstruction method that inverts dMRI measurements.<n>Spinverse represents tissue on a fixed tetrahedral grid and treats each interior face permeability as a learnable parameter.<n>It reconstructs diverse geometries and demonstrates that sequence scheduling and regularization are critical to avoid outline-only solutions.
  arXiv  Detail & Related papers  (2026-03-04T21:57:40Z)
• Suppressing Prior-Comparison Hallucinations in Radiology Report Generation via Semantically Decoupled Latent Steering [94.37535002230504]
  We develop a training-free, inference-time control framework termed Semantically Decoupled Latent Steering.<n>Our approach constructs a semantic-free intervention vector via large language model (LLM)-driven semantic decomposition.<n>We show that our approach significantly reduces the probability of historical hallucinations.
  arXiv  Detail & Related papers  (2026-02-27T04:49:01Z)
• Knowledge-Informed Kernel State Reconstruction for Interpretable Dynamical System Discovery [46.9843470803458]
  MAAT (Model Aware Approximation of Trajectories) is a framework for symbolic discovery built on knowledge-informed Kernel State Reconstruction.<n>It substantially reduces state-estimation MSE for trajectories and derivatives used by downstream symbolic regression.
  arXiv  Detail & Related papers  (2026-01-29T21:15:52Z)
• SIGMA: Scalable Spectral Insights for LLM Collapse [51.863164847253366]
  We introduce SIGMA (Spectral Inequalities for Gram Matrix Analysis), a unified framework for model collapse.<n>By utilizing benchmarks that deriving and deterministic bounds on the matrix's spectrum, SIGMA provides a mathematically grounded metric to track the contraction of the representation space.<n>We demonstrate that SIGMA effectively captures the transition towards states, offering both theoretical insights into the mechanics of collapse.
  arXiv  Detail & Related papers  (2026-01-06T19:47:11Z)
• A Physics-Informed Loss Function for Boundary-Consistent and Robust Artery Segmentation in DSA Sequences [6.154694408048338]
  We propose a novel textitPhysics-Informed Loss (PIL) that models the interaction between the predicted and ground-truth boundaries.<n>PIL consistently outperforms conventional loss functions such as Cross-Entropy, Dice, Active Contour, and Surface losses.
  arXiv  Detail & Related papers  (2025-11-25T17:08:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.