SCMA: Structure-Conditioned and Metal-Aware Flow Matching for CT Metal Artifact Reduction

In X-ray CT, metallic objects cause beam hardening, photon starvation, and scattering, leading to projection inconsistency, streaks, dark bands, and structural distortions that compromise clinical diagnosis and quantitative analysis. Existing metal artifact reduction (MAR) methods remain limited: optimization-based methods may leave residual artifacts or blur structures, regression networks may generalize poorly across scenarios, and generative models without sample-specific structural guidance and physical constraints may produce anatomically inconsistent structures. Flow Matching learns a continuous-time velocity field that deterministically transports a source distribution to a target distribution, providing a flexible MAR prior. However, standard unconditional Flow Matching does not exploit sample-specific structure, spatially nonuniform metal-induced degradation, or measured projections. To address these limitations, we propose SCMA, a structure-conditioned and metal-aware Flow Matching framework. First, a linear-interpolation-corrected image is fed into the velocity network with the intermediate state as a sample-specific structural condition, guiding inference toward artifact-free CT images while preserving anatomy. Second, time-varying spatial weights from the metal mask and its distance transform are incorporated into the Flow Matching loss to emphasize severe degradation within and around metal regions. Finally, conditional Flow Matching updates alternate with projection-consistency correction during inference, allowing reliable measurements outside metal traces to constrain predictions. Experiments on simulated and real CT data demonstrate that SCMA more effectively suppresses metal artifacts, preserves local anatomical structures, and reduces hallucination-like structures inconsistent with projection measurements than representative MAR methods.

LUCID: Learned Undersampling-Adaptive Consistency-Guided Inference with Deterministic Flow Matching for Sparse-View CT Reconstruction

Sparse-view CT reduces radiation dose and scanning time by acquiring fewer projection views, but angular undersampling makes reconstruction severely ill-posed, causing streak artifacts, structural blurring, and loss of fine details. Existing supervised methods are often tied to specific sampling settings, whereas generative methods may introduce anatomically inconsistent hallucination-like structures under severe undersampling. We propose Lucid, a sparsity-adaptive, consistency-guided reconstruction framework based on a Flow Matching generative prior for sparse-view CT. Lucid is trained only on high-quality CT images to learn a continuous transport between a Gaussian distribution and the high-quality CT image distribution, independent of view sampling. During inference, the sampling sparsity level is explicitly incorporated to adapt the generative trajectory of a single pretrained model. Specifically, Lucid constructs a degradation-matched initial state by sparsity-weighted fusion of the sparse-view FBP image and Gaussian noise, performs sparsity-modulated Flow Matching updates, and applies projection-domain data-consistency correction after each prior update. Experiments under multiple sparse-view settings show that Lucid achieves stable reconstruction performance across different sampling densities, improves image quality and structural fidelity, and reduces the risk of hallucination-like structures in generative sparse-view CT reconstruction.

Beyond Fixed Inference: Quantitative Flow Matching for Adaptive Image Denoising

Diffusion and flow-based generative models have shown strong potential for image restoration. However, image denoising under unknown and varying noise conditions remains challenging, because the learned vector fields may become inconsistent across different noise levels, leading to degraded restoration quality under mismatch between training and inference. To address this issue, we propose a quantitative flow matching framework for adaptive image denoising. The method first estimates the input noise level from local pixel statistics, and then uses this quantitative estimate to adapt the inference trajectory, including the starting point, the number of integration steps, and the step-size schedule. In this way, the denoising process is better aligned with the actual corruption level of each input, reducing unnecessary computation for lightly corrupted images while providing sufficient refinement for heavily degraded ones. By coupling quantitative noise estimation with noise-adaptive flow inference, the proposed method improves both restoration accuracy and inference efficiency. Extensive experiments on natural, medical, and microscopy images demonstrate its robustness and strong generalization across diverse noise levels and imaging conditions.

General Explicit Network (GEN): A novel deep learning architecture for solving partial differential equations

Machine learning, especially physics-informed neural networks (PINNs) and their neural network variants, has been widely used to solve problems involving partial differential equations (PDEs). The successful deployment of such methods beyond academic research remains limited. For example, PINN methods primarily consider discrete point-to-point fitting and fail to account for the potential properties of real solutions. The adoption of continuous activation functions in these approaches leads to local characteristics that align with the equation solutions while resulting in poor extensibility and robustness. A general explicit network (GEN) that implements point-to-function PDE solving is proposed in this paper. The "function" component can be constructed based on our prior knowledge of the original PDEs through corresponding basis functions for fitting. The experimental results demonstrate that this approach enables solutions with high robustness and strong extensibility to be obtained.