Progressive Divide-and-Conquer via Subsampling Decomposition for Accelerated MRI

Deep unfolding networks (DUN) have emerged as a pop-ular iterative framework for accelerated magnetic reso-nance imaging (MRI) reconstruction. However, conventional DUN aims to reconstruct all the missing information within the entire null space in each iteration. Thus it could be challenging when dealing with highly ill-posed degradation, often resulting in subpar reconstruction. In this work, we propose a Progressive Divide-And-Conquer (PDAC) strategy, aiming to break down the subsampling process in the actual severe degradation and thus per-form reconstruction sequentially. Starting from decomposing the original maximum-a-posteriori problem of accel-erated MRI, we present a rigorous derivation of the pro-posed PDAC framework, which could be further unfolded into an end-to-end trainable network. Each PDAC iter-ation specifically targets a distinct segment of moderate degradation, based on the decomposition. Furthermore, as part of the PDAC iteration, such decomposition is adaptively learned as an auxiliary task through a degradation predictor which provides an estimation of the decomposed sampling mask. Following this prediction, the sampling mask is further integrated via a severity conditioning mod-ule to ensure awareness of the degradation severity at each stage. Extensive experiments demonstrate that our pro-posed method achieves superior performance on the pub-licly available fastMRI and Stanford2D FSE datasets in both multi-coil and single-coil settings. Code is available at https://github.com/ChongWang1024/PDAC.