DH-Mamba: Exploring Dual-domain Hierarchical State Space Models for MRI Reconstruction

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.