Progressive Divide-and-Conquer via Subsampling Decomposition for
  Accelerated MRI
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 null space in each iteration. Thus it could be challenging when dealing
with highly ill-posed degradation, usually leading to unsatisfactory
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. Specifically, each
iterative stage in PDAC focuses on recovering a distinct moderate degradation
according to 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.