Progressive Divide-and-Conquer via Subsampling Decomposition for Accelerated MRI
Authors: Chong Wang, Lanqing Guo, Yufei Wang, Hao Cheng, Yi Yu, Bihan Wen

Deep unfolding networks (DUN) have emerged as a popular iterative framework for accelerated magnetic resonance imaging (MRI) reconstruction. However conventional DUN aims to reconstruct all the missing information within the entire 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 perform reconstruction sequentially. Starting from decomposing the original maximum-a-posteriori problem of accelerated MRI we present a rigorous derivation of the proposed PDAC framework which could be further unfolded into an end-to-end trainable network. Each PDAC iteration 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 module to ensure awareness of the degradation severity at each stage. Extensive experiments demonstrate that our proposed method achieves superior performance on the publicly available fastMRI and Stanford2D FSE datasets in both multi-coil and single-coil settings.