Accelerated MRI Reconstruction Using a Diffusion Model based on the Divide-and-Conquer Strategy

Abstract

In this study, we present a novel framework for accelerated MRI reconstruction that introduces posterior probability sampling based on diffusion models within a divide-and-conquer strategy. In accelerated MRI, patient anatomy must be reconstructed from under-sampled k-space measurements, which makes the problem inherently ill-posed. To address this problem, prior knowledge is incorporated to restrict the solution space and improve the fidelity of the reconstructed images. Specifically, we employ a prior probability distribution modeled by a diffusion process to constrain reconstruction. For each posterior sample, the Fourier transform image is analyzed, and reconstruction accuracy is estimated as a confidence value for each frequency component. By sequentially adopting frequency sequences with higher confidence, the method progressively enhances reconstruction quality while gradually tightening constraints. Furthermore, by generating multiple reconstructions through repeated posterior sampling, we compute the pixel-wise variance of the reconstructed images. This variance serves as a statistical indicator of reconstruction reliability, allowing the confidence of individual pixels to be visualized and quantified. The proposed framework thus provides both accurate image reconstruction and an interpretable measure of uncertainty. Finally, we demonstrate the effectiveness of our method through experiments on real MRI data.