An interpretable MRI reconstruction network with two-grid-cycle correction and geometric prior distillation

Although existing deep learning compressed-sensing-based Magnetic Resonance Imaging (CS-MRI) methods have achieved considerably impressive performance, explainability and generalizability continue to be challenging for such since the transition from mathematical analysis network design not always natural enough, often most of them are flexible enough handle multi-sampling-ratio reconstruction assignments. {In this work, tackle generalizability, we propose a unifying unfolding interpretable CS-MRI framework.} The combined approach offers more than previous works whereas gains through geometric prior module. Inspired by multigrid algorithm, first embed CS-MRI-based optimization algorithm into correction-distillation scheme that consists three ingredients: pre-relaxation module, correction module distillation Furthermore, employ condition learn adaptively step-length noise level, which enables proposed framework jointly train multi-ratio tasks single model. { model only compensates lost contextual information reconstructed image is refined low frequency error in characteristic k-space}, but also integrates theoretical guarantee model-based superior performances learning-based methods. Therefore, it can give us novel perspective biomedical imaging networks. Numerical experiments show our outperforms state-of-the-art terms qualitative quantitative evaluations.} {Our method achieves 3.18 dB improvement at CS ratio 10\% average 1.42 over other comparison on brain dataset using Cartesian sampling mask.