Deep generative models have recently emerged as powerful priors for solving ill-posed inverse problems in CT, with diffusion-based approaches achieving state-of-the-art reconstruction performance. However, diffusion models typically rely on stochastic sampling procedures, long inference trajectories, and carefully tuned noise schedules, which can limit computational efficiency and numerical stability, especially at high spatial resolutions. In this work, we investigate Flow Matching as an alternative generative prior for CT reconstruction. We train a high-resolution Rectified Flow Matching model on 256x256 chest images from the Mayo Clinic Low-Dose CT dataset. To mitigate overfitting and limited anatomical variability, we employ a two-stage training strategy consisting of an initial phase with strong, anatomically informed data augmentation, followed by a fine-tuning phase with reduced or no augmentation to refine structural fidelity. The resulting model is capable of generating high-quality and anatomically coherent CT-like images, serving as a strong learned prior. We then evaluate multiple reconstruction methods specifically designed for Flow Matching models, including Plug-and-Play Flow, FlowDPS, Flower, and Flow-Priors (ICTM), and compare them against state-of-the-art diffusion-based reconstruction algorithms such as DDRM, DPS, and DiffPIR. Experimental results across several CT inverse problem settings show that Flow Matching-based approaches consistently outperform diffusion-based methods in terms of PSNR, SSIM, and perceptual quality, while requiring fewer sampling steps. Finally, we publicly release the trained Flow Matching model and accompanying code to facilitate reproducibility and future research. Overall, this work demonstrates that Flow Matching provides a stable, efficient, and effective alternative to diffusion models for high-resolution CT image reconstruction.
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.
Efe Ilıcak, Baris Imre, Chloé Najac +4eess.IV cs.CV physics.med-ph
Deep unrolled networks (DUNs) integrate physical forward models with learned regularization in cascaded network architectures, achieving exceptional performance in inverse problems while maintaining interpretability. While most DUNs operate in the object domain (e.g., image space), recent variants explored representation spaces for improved information flow. However, these methods rely on heuristic methods for data consistency (DC), sacrificing fidelity with measurements. In this work, we introduce DUNE (Deep Unrolled Networks in rEpresentation space), a framework that maintains exact adherence to physical measurements while operating in learned representation spaces. By deriving the DC gradient via the chain rule and implementing it through the Vector-Jacobian Product (VJP), we enable exact backpropagation of measurement residuals into the representation space. This formulation supports diverse architectural backbones, including pre-trained encoders to guide the iterative process. We assess DUNE against state-of-the-art baselines on accelerated MRI reconstruction tasks, demonstrating that exact VJP-based gradients yield superior reconstruction quality and structural fidelity across both single-channel portable low-field and multi-channel clinical high-field MRI acquisitions. The code will be available upon publication at https://github.com/EfeIlicak/DUNE.
We present Full-Self Diagnostics (FSD), a unified mathematical framework for recovering latent physiological states from unconstrained 9-second facial videos captured by consumer smartphones. The approach integrates five mutually reinforcing components: (1) a physics-based forward model derived from the radiative transfer equation and chromophore absorption that maps camera observables to biomarker concentrations; (2) an information-theoretic observability theory proving that multi-channel visual signals (spectral, pulse, respiratory, micro-expression, and oculomotor) contain strictly increasing mutual information with physiological state; (3) a stable, Tikhonov-regularized inverse problem with domain-uniform identifiability guarantees; (4) an operator-learning formulation that enables generalization across devices, resolutions, and populations; and (5) a supervised learning procedure, interpretable as stochastic variational inference, that continuously refines the model from paired biosensor ground truth with performance improving proportionally to one over the square root of the number of paired observations. Empirical validation on 38812 real-world paired scans across 59 subjects demonstrates practical performance. Self-collected data from the lead author (glucose range 35-550 mg/dL) yields MARD of 29.86 percent with 97.57 percent of predictions in Clarke Error Grid Zones A+B and only 0.27 percent in the dangerous Zone E. A well-managed diabetic participant achieves MARD of 17 percent in the narrower 70-180 mg/dL band. These results confirm that consumer-grade facial video encodes sufficient structured information for clinically relevant, non-invasive biomarker inference under fully unconstrained conditions, with performance scaling predictably as more paired data becomes available.
Arda Atalık, Sumit Chopra, Daniel K. Sodicksoneess.IV cs.AI cs.CV physics.med-ph
MRI provides excellent soft-tissue contrast without ionizing radiation, but long acquisition times increase patient discomfort while also raising exam costs and limiting scanner throughput. A common approach to reduce scan time is to acquire fewer measurements, which yields an ill-posed linear inverse problem; recovering diagnostic-quality images therefore requires incorporating prior knowledge beyond the measured data. In follow-up exams, the most recent prior scan of a patient can provide a highly informative subject-specific context, but practical use is complicated by temporal changes (including pathology progression), misalignment between scans, and protocol drift across acquisitions. In this work, we introduce L-TGVN, a Longitudinal Trust-Guided Variational Network that leverages prior scans as side information to reconstruct the current scan from heavily undersampled measurements. Crucially, L-TGVN constrains the influence of prior scans to be consistent with the acquired measurements. Unlike many existing longitudinal reconstruction methods, it does not require explicit pre-registration between prior and current scans. It further accommodates differences in acquisition protocols across visits (e.g., changes in sequence parameters). We evaluate L-TGVN against matched-capacity baselines, including prior-guided methods and methods that do not use longitudinal priors, and observe consistent improvements in standard quantitative metrics together with better preservation of fine structures at challenging accelerations. Source code is available at github.com/sodicksonlab/L-TGVN.
Generative models are increasingly used as priors for inverse problems, but their ability to produce realistic images creates a basic trust problem: a plausible reconstruction may be supported by the measurements, or it may be filled in by the prior along unobserved directions. This distinction is especially important in medical imaging, where acquisition operators are designed under scan-time, dose, and calibration constraints. We study generative inverse problems from a measurement-geometry perspective. The central question is whether a fixed measurement operator can distinguish nearby images that are plausible under the generative prior, and whether this relationship can guide better measurements. We introduce a local measurement-manifold compatibility measure that quantifies how well the operator observes prior-relevant tangent directions. Under local regularity assumptions, we prove that this quantity controls the stable part of the reconstruction error, while the generative prior controls off-manifold drift. This worst-direction certificate motivates practical fixed and sequential acquisition rules based on overall local volume preservation, including a posterior-cloud design that adapts measurements at test time without training a sampling policy. Across row-sampling, tomographic, and MR acquisition settings, the proposed scores predict failure modes, explain measurement-induced hallucinations, and guide better sampling. In fastMRI Cartesian sampling, posterior-cloud measurement design improves over strong non-learned ACS-preserving baselines, including variable-density and Poisson-like masks.