The accelerated MRI reconstruction poses a challenging ill-posed inverse problem due to the significant undersampling in k-space. Deep neural networks, such as CNNs and ViTs, have shown substantial performance improvements for this task while encountering the dilemma between global receptive fields and efficient computation. To this end, this paper explores selective state space models (Mamba), a new paradigm for long-range dependency modeling with linear complexity, for efficient and effective MRI reconstruction. However, directly applying Mamba to MRI reconstruction faces three significant issues: (1) Mamba typically flattens 2D images into distinct 1D sequences along rows and columns, disrupting k-space's unique spectrum and leaving its potential in k-space learning unexplored. (2) Existing approaches adopt multi-directional lengthy scanning to unfold images at the pixel level, leading to long-range forgetting and high computational burden. (3) Mamba struggles with spatially-varying contents, resulting in limited diversity of local representations. To address these, we propose a dual-domain hierarchical Mamba for MRI reconstruction from the following perspectives: (1) We pioneer vision Mamba in k-space learning. A circular scanning is customized for spectrum unfolding, benefiting the global modeling of k-space. (2) We propose a hierarchical Mamba with an efficient scanning strategy in both image and k-space domains. It mitigates long-range forgetting and achieves a better trade-off between efficiency and performance. (3) We develop a local diversity enhancement module to improve the spatially-varying representation of Mamba. Extensive experiments are conducted on three public datasets for MRI reconstruction under various undersampling patterns. Comprehensive results demonstrate that our method significantly outperforms state-of-the-art methods with lower computational cost.

翻译：加速磁共振成像重建因k空间的严重欠采样而构成一个具有挑战性的病态逆问题。深度神经网络，如CNN和ViT，在此任务上已展现出显著的性能提升，但同时也面临着全局感受野与高效计算之间的困境。为此，本文探索了选择性状态空间模型（Mamba）这一具有线性复杂度、用于长程依赖建模的新范式，以实现高效且有效的磁共振成像重建。然而，直接将Mamba应用于磁共振成像重建面临三个显著问题：(1) Mamba通常将二维图像沿行和列展开为独立的一维序列，这破坏了k空间独特的光谱特性，且未充分挖掘其在k空间学习中的潜力。(2) 现有方法采用多方向长程扫描在像素级展开图像，导致长程遗忘和高计算负担。(3) Mamba难以处理空间变化的内容，导致局部表示多样性有限。为解决这些问题，我们从以下角度提出了一种用于磁共振成像重建的双域分层Mamba：(1) 我们率先将视觉Mamba引入k空间学习。为光谱展开定制了循环扫描策略，有利于k空间的全局建模。(2) 我们在图像域和k空间域均提出了一种采用高效扫描策略的分层Mamba。它缓解了长程遗忘问题，并在效率与性能之间实现了更好的平衡。(3) 我们开发了一个局部多样性增强模块，以改善Mamba对空间变化内容的表示能力。我们在三个公开数据集上针对多种欠采样模式进行了广泛的磁共振成像重建实验。综合结果表明，我们的方法以更低的计算成本显著超越了现有最先进方法。