# DH-Mamba: Exploring Dual-domain Hierarchical State Space Models for MRI Reconstruction arXiv: https://arxiv.org/abs/2501.08163 ยท HTML: https://mlsanity.com/paper/2501.08163/ ## Key facts - Cited by 3 papers in the map (data through 14 Oct 2026). - Placed in Mamba for medical image analysis, one of 10 directions in State-space sequence models (S4, Mamba). - Builds on 49 of its 83 references that are in the map. - First posted on arXiv 14 Jan 2025. ## Placed in - State-space sequence models (S4, Mamba) / [Mamba for medical image analysis](https://mlsanity.com/ssm/mamba-for-medical-image-analysis/) ## Builds on (most cited first, 30 of 49) - [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020) - [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023) - [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024) - [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022) - [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020) - [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022) - [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018) - [A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospects](https://mlsanity.com/paper/2004.02806/) (2020) - [MambaIR: A Simple Baseline for Image Restoration with State-Space Model](https://mlsanity.com/paper/2402.15648/) (2024) - [How Do Vision Transformers Work?](https://mlsanity.com/paper/2202.06709/) (2022) - [LocalMamba: Visual State Space Model with Windowed Selective Scan](https://mlsanity.com/paper/2403.09338/) (2024) - [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017) - [A Survey of the Recent Architectures of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1901.06032/) (2019) - [An Empirical Study of Mamba-based Language Models](https://mlsanity.com/paper/2406.07887/) (2024) - [Swin-UMamba: Mamba-based UNet with ImageNet-based pretraining](https://mlsanity.com/paper/2402.03302/) (2024) - [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022) - [MambaIRv2: Attentive State Space Restoration](https://mlsanity.com/paper/2411.15269/) (2024) - [VL-Mamba: Exploring State Space Models for Multimodal Learning](https://mlsanity.com/paper/2403.13600/) (2024) - [VmambaIR: Visual State Space Model for Image Restoration](https://mlsanity.com/paper/2403.11423/) (2024) - [MedMamba: Vision Mamba for Medical Image Classification](https://mlsanity.com/paper/2403.03849/) (2024) - [Unsupervised MRI Reconstruction via Zero-Shot Learned Adversarial Transformers](https://mlsanity.com/paper/2105.08059/) (2021) - [DuDoRNet: Learning a Dual-Domain Recurrent Network for Fast MRI Reconstruction with Deep T1 Prior](https://mlsanity.com/paper/2001.03799/) (2020) - [Towards performant and reliable undersampled MR reconstruction via diffusion model sampling](https://mlsanity.com/paper/2203.04292/) (2022) - [FreqMamba: Viewing Mamba from a Frequency Perspective for Image Deraining](https://mlsanity.com/paper/2404.09476/) (2024) - [Swin Transformer for Fast MRI](https://mlsanity.com/paper/2201.03230/) (2022) - [Vision Mamba: A Comprehensive Survey and Taxonomy](https://mlsanity.com/paper/2405.04404/) (2024) - [ReconFormer: Accelerated MRI Reconstruction Using Recurrent Transformer](https://mlsanity.com/paper/2201.09376/) (2022) - [nnMamba: 3D Biomedical Image Segmentation, Classification and Landmark Detection with State Space Model](https://mlsanity.com/paper/2402.03526/) (2024) - [MaIR: A Locality- and Continuity-Preserving Mamba for Image Restoration](https://mlsanity.com/paper/2412.20066/) (2024) - [SKM-TEA: A Dataset for Accelerated MRI Reconstruction with Dense Image Labels for Quantitative Clinical Evaluation](https://mlsanity.com/paper/2203.06823/) (2022) ## Built on by (most cited first, 3 of 3) - [FLAT: FLow-Aligned Training of Unrolled Networks for MRI Reconstruction](https://mlsanity.com/paper/2512.03020/) (2025) - [Frequency Error-Guided Under-sampling Optimization for Multi-Contrast MRI Reconstruction](https://mlsanity.com/paper/2601.09316/) (2026) - [Revisiting Global Token Mixing in Task-Dependent MRI Restoration: Insights from Minimal Gated CNN Baselines](https://mlsanity.com/paper/2603.01449/) (2026) ## Abstract (arXiv) 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.