A Deep Framework Assembling Principled Modules for CS-MRI: Unrolling Perspective, Convergence Behaviors, and Practical Modeling

Compressed Sensing Magnetic Resonance Imaging (CS-MRI) significantly accelerates MR acquisition at a sampling rate much lower than the Nyquist criterion. A major challenge for CS-MRI lies in solving the severely ill-posed inverse problem to reconstruct aliasing-free MR images from the sparse k -space data. Conventional methods typically optimize an energy function, producing restoration of high quality, but their iterative numerical solvers unavoidably bring extremely large time consumption. Recent deep techniques provide fast restoration by either learning direct prediction to final reconstruction or plugging learned modules into the energy optimizer. Nevertheless, these data-driven predictors cannot guarantee the reconstruction following principled constraints underlying the domain knowledge so that the reliability of their reconstruction process is questionable. In this paper, we propose a deep framework assembling principled modules for CS-MRI that fuses learning strategy with the iterative solver of a conventional reconstruction energy. This framework embeds an optimal condition checking mechanism, fostering efficient and reliable reconstruction. We also apply the framework to three practical tasks, i.e., complex-valued data reconstruction, parallel imaging and reconstruction with Rician noise. Extensive experiments on both benchmark and manufacturer-testing images demonstrate that the proposed method reliably converges to the optimal solution more efficiently and accurately than the state-of-the-art in various scenarios.