Parallel Trajectory Constraint Sampling for Solving Universal Medical Inverse Problems

Inverse problems in medical imaging, such as undersampled magnetic resonance imaging (MRI) and sparse-view computed tomography (CT) reconstruction, are essential yet challenging tasks for achieving accurate and reliable diagnostic images. Traditional reconstruction approaches, including iterative optimization algorithms and supervised deep learning methods, often struggle with limited adaptability across imaging protocols, substantial computational requirements, and poor generalization between different imaging modalities. Diffusion-based generative models have recently demonstrated promising results; however, these methods frequently suffer from cumulative estimation errors in their sampling processes, limiting their practical performance and robustness. In this paper, we propose a novel framework called Parallel Trajectory Constrained Sampling (PCS), which substantially enhances image reconstruction quality by explicitly enforcing consistency with the underlying physical measurement process. Specifically, PCS introduces a measurement-domain diffusion model whose reverse stochastic differential equation (SDE) trajectory is analytically determinable, thus obviating the need for a learned score estimator within the measurement domain. Furthermore, a parallel trajectory constraint is formulated to rigorously align the reverse sampling paths of the measurement and image diffusion processes, ensuring strict adherence to the known physical model at every sampling step. The proposed PCS method is flexible and can seamlessly integrate various SDE-based diffusion priors. Extensive experiments on representative inverse problems—including undersampled MRI reconstruction, sparse-view CT reconstruction, and image super-resolution—demonstrate that PCS consistently outperforms existing state-of-the-art diffusion-based reconstruction methods. Although current evaluations focus specifically on MRI and CT modalities, the PCS framework holds considerable promise for broader applicability to other imaging modalities and inverse problems, which we plan to investigate in future studies.