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

翻译：尽管基于深度学习的压缩感知磁共振成像（CS-MRI）方法已取得显著性能，但其可解释性和泛化能力仍面临挑战——由于从数学分析到网络设计的过渡往往不够自然，多数方法难以灵活处理多采样率重建任务。为应对可解释性与泛化性问题，本文提出一种统一的深度展开多采样率可解释CS-MRI框架。该方法通过几何先验模块赋予深度学习可解释性，同时比现有方法具有更强的泛化能力。受多重网格算法启发，我们首先将基于CS-MRI的优化算法嵌入校正-蒸馏方案中，该方案包含三个组件：预松弛模块、校正模块和几何先验蒸馏模块。进一步，我们采用条件模块自适应学习步长和噪声水平，使所提框架能够通过单一模型联合训练多比率任务。该模型不仅通过几何特征k空间中低频误差的校正补偿了重建图像丢失的上下文信息，还融合了基于模型方法的理论保证与基于深度学习方法的重建性能优势，为生物医学成像网络设计提供了新视角。数值实验表明，本框架在定性与定量评估中均优于现有最优方法。采用笛卡尔采样掩膜时，在脑部数据集上，本方法在10%低采样率下信噪比提升3.18 dB，相较于其他对比方法平均提升1.42 dB。