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

T0 review · 1 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A dual-domain Mamba that scans k-space in concentric circles reconstructs undersampled MRI to 39.32 dB PSNR at 4x acceleration, beating prior methods by more than 3 dB at lower computational cost.

desk verdict Solid Mamba-for-MRI architecture paper with careful ablations, but the impossible NMSE in Table III undercuts the multi-coil claim until fixed. read the letter →

arxiv 2501.08163 v3 pith:SQ6B74Y4 submitted 2025-01-14 eess.IV cs.CV

Yucong Meng , Zhiwei Yang , Zhijian Song , Yonghong Shi This is my paper · ORCID
classification eess.IVcs.CV
keywords MRIreconstructionMambastatespacemodelk-spacecircularscanninghierarchicalcompressedsensingaccelerated
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that adapting the Mamba sequence model to the structure of MRI data, processing both the image and its Fourier-domain k-space spectrum, makes accelerated MRI reconstruction substantially more accurate and cheaper than current CNN, transformer, and vanilla Mamba approaches. The method, DH-Mamba, scans k-space along concentric circular paths from low to high frequency rather than row by row, uses a hierarchical scan that keeps one high-resolution path and three downsampled paths to avoid long-range forgetting, and adds a pixel-wise gating module for local feature diversity. On the CC359 brain dataset at 4x acceleration it reports 39.32 dB PSNR, more than 3 dB above the best prior method, with 117 GFLOPs and 1.87M parameters, and it also leads on fastMRI and SKM-TEA. If correct, the work suggests that the ordering of tokens fed to a state space model should respect the native structure of the signal, not just the image grid.

What carries the argument

The load-bearing object is DH-Mamba, a dual-branch network whose design is organized around how MRI data is arranged. In the k-space branch, the key mechanism is circular scanning: instead of unfolding a 2D spectrum row by row, the spectrum is traced along four concentric, frequency-ordered paths so that low frequencies at the center are read before high frequencies at the periphery, preserving the concentric structure of k-space and giving the S6 state space model a sequence whose order encodes spectral proximity. In both branches, hierarchical scanning divides the four scan directions into one high-resolution path and three low-resolution paths with $s=2$ downsampling, processed by separate S6 blocks and upsampled back, which shortens sequence length to counter long-range forgetting and reduces cost. The local enhancement module replaces the usual MLP with a pixel-wise gating mask multiplied against local convolution features, reintroducing spatially varying detail. Together these mechanisms let the model keep a global receptive field at linear complexity.

What would settle it

Train the k-space branch with the circular scan replaced by a random fixed permutation of the same tokens, a spiral-from-center order, or a standard row-and-column scan while keeping every other component identical; if PSNR on CC359 at 4x stays within a few tenths of a decibel of 39.32, the claim that frequency-ordered circular unfolding is essential would be falsified. Likewise, if the gain over the best transformer baseline shrinks or vanishes on a dataset with non-Cartesian sampling, the k-space ordering claim would be pattern-specific rather than general.

Watch

Extended reading notes

Core claim

On its own terms, the central discovery is that Mamba's selective state space mechanism works for MRI reconstruction when it is applied in both the image domain and the k-space domain, with scans designed for each domain. The k-space branch Fourier-transforms features, unfolds the spectrum along four concentric circular paths ordered from low to high frequency, processes those sequences with S6 blocks, and transforms back; the image branch uses standard row and column scans. A hierarchical scan splits the four directions so only one operates at full resolution while the other three run on downsampled maps, shortening sequences and reducing the forgetting of early tokens. A local enhancement module multiplies convolution-derived features by a learnable pixel-wise gate to restore spatial variation that Mamba's linear aggregation suppresses. The paper reports consistent gains over previous state of the art across three public datasets, multiple acceleration factors, and Cartesian, radial, and random undersampling masks, with lower FLOPs and parameters than the strongest baselines.

Load-bearing premise

The load-bearing premise is that unfolding k-space along concentric frequency-ordered circular paths is a better input order for Mamba than row-and-column scans, but the paper gives no proof that this ordering is optimal, only an ablation showing it helps by 0.56 dB; if the benefit came instead from the extra k-space branch or the hierarchical downsampling, the circular-scan argument would not carry the result.

Editorial extensions

If this is right

  • If correct, DH-Mamba establishes that Mamba-based architectures can beat transformer-based ones on accelerated MRI, not just match them, while using less computation than both.
  • The ablation showing a 0.98 dB drop when the k-space branch is removed implies that explicitly modeling the frequency layout of k-space is itself worth close to a decibel of PSNR.
  • The chosen 3:1 ratio of low-resolution to high-resolution scan paths is presented as the best trade-off point: four high-resolution paths cost 203 GFLOPs and give 39.14 dB, while four low-resolution paths drop to 38.27 dB, so the hierarchy balances detail against long-range forgetting.
  • The method reports gains across Cartesian, radial, and random masks and across single-coil and multi-coil data, which would make the design independent of any one sampling geometry.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: circular scanning is a general recipe, not an MRI-specific trick; any inverse problem whose signal lives in a Fourier-like or polar-ordered domain could benefit from ordering tokens by frequency radius instead of raster order.
  • Editorial inference: the paper's own discussion admits that Mamba's causality is a ceiling, so a bidirectional or non-causal variant that can read both earlier and later tokens along the circular path is a natural next step and might close the remaining gap to ground truth.
  • Editorial inference: the 3:1 LR/HR path ratio is chosen empirically, and the optimal ratio likely depends on image resolution and anatomy, so a learned or adaptive allocation of scan paths across scales is a testable extension.
  • Editorial inference: the claim to pioneer Mamba in k-space should be read narrowly; the novelty is the circular scan and the dual-domain combination, not the use of Mamba itself, and the most informative future comparison is against other k-space-aware SSM scans under identical training budgets.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 6 minor

Summary. The paper proposes DH-Mamba, a dual-domain hierarchical state space model for accelerated MRI reconstruction. The method combines a k-space branch with a circular scanning strategy designed to respect the concentric frequency structure of k-space, an image-space branch using standard Mamba scanning, a hierarchical scanning strategy that processes one high-resolution path and three downsampled paths to reduce sequence length, and a local enhancement module (LEM) that applies a pixel-wise gating mask to increase local feature diversity. The architecture is evaluated on three public datasets (CC359, fastMRI, SKM-TEA) under Cartesian, radial, and random undersampling masks at acceleration factors 4 and 8 (and additional factors in the mask experiments). The central claim is that DH-Mamba consistently outperforms prior CNN-, transformer-, and Mamba-based methods while using lower computation (117 GFLOPs versus 342 G for ReconFormer and 190 G for MambaIR).

Significance. If the reported results are correct, DH-Mamba is a practically relevant contribution: it demonstrates that a Mamba-based architecture can be effectively adapted to the k-space domain, and the ablations support the contribution of each proposed component (circular k-space scan, hierarchical scanning, and local enhancement). The efficiency numbers are attractive, and the qualitative improvements shown are consistent with the quantitative gains on CC359 and fastMRI. However, the multi-coil results on SKM-TEA contain a physically impossible NMSE value that undermines the claim of consistent superiority until it is corrected and the surrounding numbers are re-verified. The paper does not yet release code, so the numbers cannot be independently checked.

major comments (1)
  1. [Table III (SKM-TEA)] The NMSE entry for DH-Mamba at 8x acceleration factor is internally impossible. NMSE is non-negative, so the reported mean of 0.0020 with standard deviation 0.0032 implies a negative lower tail, and the mean is roughly eight times smaller than the AF=4 NMSE (0.0156) despite a lower PSNR (32.97 dB vs 35.43 dB). This is almost certainly a transcription error (e.g., 0.0202 or 0.0220), but as printed it invalidates the reported AF=8 multi-coil comparison and weakens the claim that DH-Mamba 'consistently surpasses' prior methods on SKM-TEA. The authors must correct this entry, re-check all metrics in Table III, and reperform the comparison against ReconFormer (whose AF=8 NMSE is 0.0239) once the correct value is established.
minor comments (6)
  1. [Section III-C1] The text says 'a circular scanning scheme is deigned'—this should read 'designed'.
  2. [Table III] The standard deviation for DH-Mamba SSIM at AF=8 (0.0025) is an order of magnitude smaller than at AF=4 (0.0232) and also much smaller than the corresponding values for other methods; please verify that this is not a typographical error.
  3. [Figure 9 caption] The caption states 'A lager ERF is indicated'—this should read 'A larger ERF'.
  4. [Throughout] The name of the transformer baseline is written inconsistently as 'ReconFormer' and 'Reconformer'; please standardize the spelling.
  5. [Related Work and Section III-C1] The paper claims to 'pioneer vision Mamba in k-space learning' while citing MambaMIR and MMR-Mamba; please clarify explicitly how the proposed k-space circular scanning differs from any k-space processing in those methods, since the novelty claim is currently only implicit.
  6. [Table V] The ablation table uses check marks to denote enabled components, but the rows do not clearly indicate which component is removed; for example, row (a) is described as removing the image branch, yet all columns appear checked. Please use explicit labels such as 'w/o Img.' to make the ablation settings unambiguous.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's contributions are empirical architecture components evaluated on held-out test data, and the self-citations are not load-bearing.

full rationale

This is an empirical deep-learning paper. The proposed DH-Mamba is a neural architecture with hand-designed components (circular k-space scanning, hierarchical scanning, local enhancement module), trained on public MRI data and evaluated on held-out test sets. There is no equation in the paper that reduces to the method's own inputs, no fitted parameter that is later renamed as a prediction, and no uniqueness theorem or ansatz imported from the authors' prior work to force the design. The self-citations ([12], [38], [39], [40]) appear only in the related-work survey and do not ground any central claim. The quantitative results are measured on external benchmarks, so the central claim of superiority is empirically checkable rather than circular. The ablation studies are also independent: they compare the proposed modules against alternative designs (SS2D, Window-SS2D, Continuous-SS2D, MLP, CAB) and show incremental performance differences, which is consistent with an empirical architecture paper. The suspicious Table III entry (NMSE 0.0020 ± 0.0032 at AF=8 on SKM-TEA) is an internal-consistency / correctness concern, not a circularity concern, because it does not arise from the method being equivalent to its inputs; it is a reported number that should be verified. Under the rubric, non-finding is appropriate.

Assumptions & free parameters 6 free parameters · 3 assumptions · 0 invented entities

The method introduces no new physical entities. It relies on standard signal processing (FFT), Mamba primitives, and empirically chosen hyperparameters. The main assumptions are about the structure of k-space and the sufficiency of downsampling for global context.

free parameters (6)
  • channel dimension C = 64
    Empirically set; not derived from theory.
  • state size H of S6 = 16
    Default from Mamba; not tuned per dataset.
  • number of DHM groups M = 6
    Chosen by hand; not optimized systematically.
  • number of DHM blocks N = 6
    Chosen by hand; not optimized systematically.
  • hierarchical downsampling stride s = 2
    Selected after ablations; affects LR path resolution.
  • number of LR scanning paths = 3
    Selected after ablation in Table VII; trade-off between performance and compute.
assumptions (3)
  • domain assumption k-space has a concentric frequency structure with low frequencies at the center
    Invoked to justify the circular scanning design in Section III.C.1; true for MRI but the ideal scan order is not proven optimal.
  • domain assumption Downsampled feature maps preserve coarse global context needed for reconstruction
    Invoked for hierarchical scanning; supported by ablation but not a formal guarantee.
  • standard math FFT and IFFT operations are exact and invertible in the network
    Used in dual-domain branches; standard property.

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Cite this review

Pith. "Pith review of DH-Mamba: Exploring Dual-domain Hierarchical State Space Models for MRI Reconstruction." pith.science (2026). https://pith.science/paper/SQ6B74Y4

@misc{pith2026250108163,
  author       = {Pith},
  title        = {Pith review of: DH-Mamba: Exploring Dual-domain Hierarchical State Space Models for MRI Reconstruction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SQ6B74Y4}},
  note         = {Machine review of arXiv:2501.08163}
}
read the original abstract

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.

Figures

Figures reproduced from arXiv: 2501.08163 by the authors.

Figure 1
Figure 1. Our main idea. (a) Applying vanilla Mamba into MRI reconstruction [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. (a) The overall architecture of the proposed DH-Mamba, which can be divided into three stages, i.e., shallow extraction, deep extraction, and high [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Architecture of the proposed local enhancement module (LEM). [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Visualization comparison on the single-coil datasets, including (a) the CC359 dataset and (b) the fastMRI dataset. The first row of each subplot shows [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Visualization comparison on the multi-coil SKM-TEA dataset. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 7
Figure 7. Figure 7: Visualization comparison of different methods under more undersam [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Illustration of the long-range forgetting using general SS2D method [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.