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LMO: Linear Mamba Operator for MRI Reconstruction
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Proposes the Linear Mamba Operator (LMO), a neural operator that combines SSM-based scanning integration and convolution integration to reconstruct MRI with linear complexity and strong generalization across acceleration rates.
Problem
MRI reconstruction from undersampled k-space suffers from poor data consistency, weak interpretability, and catastrophic generalization when acceleration rate changes at test time.
Approach
Treats MRI reconstruction as learning a mapping between bandlimited function spaces using a neural operator whose kernel integral is split into a Mamba-style scanning integral (SSM, global) and a local convolution integral, giving continuous-discrete equivalence and O(n) cost.
Key results
- Under x4 radial acceleration on IXI, LMO reaches 48.16 dB PSNR / 0.996 SSIM, above PGIUN (47.09 dB) and H-DSLR (45.31 dB).
- LMO is reported as the only method whose performance improves when trained at x8 and tested at lower acceleration (x8 to x4: 43.50 dB vs 29.80 dB for PGIUN).
- Ablation: pure convolution integration drops PSNR by 13.48 dB and pure scanning integration by 7.71 dB relative to the combined model.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LMO instead of PGIUN | MRI reconstruction · IXI radial ×4 | PSNR (dB): 47.09 -> 48.16 | Helped |
| Use LMO instead of PGIUN | MRI reconstruction · Multi-coil ×6 | PSNR (dB): 40.33 -> 41.52 | Helped |
| Add scanning integration to convolution integration (ablation) | LMO · IXI radial ×4 | PSNR (dB): 34.68 -> 48.16 | Helped |
| Add convolution integration to scanning integration (ablation) | LMO · IXI radial ×4 | PSNR (dB): 40.45 -> 48.16 | Helped |
| Train at ×8 and test at ×4 instead of using PGIUN | LMO · IXI radial ×8 to ×4 | PSNR (dB): 29.80 -> 43.50 | Helped |
| Train at ×4 and test at ×8 instead of using H-DSLR | LMO · IXI radial ×4 to ×8 | PSNR (dB): 24.10 -> 30.25 | Helped |
Surprising findings
- LMO shows improved performance when trained at higher acceleration and tested at lower acceleration, which the authors describe as unique among compared methods.
Limitations
- Evaluation limited to brain and knee MRI datasets; applicability to other modalities left to future work.
- Theoretical derivations assume simplified constant parameters in the kernel before learning them from data.
Experimental setup
Datasets: IXI fastMRI knee multi-coil brain dataset (Aggarwal et al.)
Benchmarks: IXI fastMRI knee multi-coil brain dataset
Metrics: PSNR SSIM FLOPs Params
Baselines: Unet SwinIR U-Mamba HQS-Net H-DSLR PGIUN
Builds on: Fourier neural operator Mamba Convolutional neural operator Deep unrolling networks Zero-order hold discretization
Closest papers by meaning
- Demystify Mamba in Vision: A Linear Attention Perspective (NeurIPS 2024 · similarity 0.83)
- Breaking Information Isolation: Accelerating MRI via Inter-sequence Mapping and Progressive Masking (AAAI 2025 · similarity 0.83)
- Efficient Noise Calculation in Deep Learning-based MRI Reconstructions (ICML 2025 · similarity 0.83)
- Boosting ViT-based MRI Reconstruction from the Perspectives of Frequency Modulation, Spatial Purification, and Scale Diversification (AAAI 2025 · similarity 0.83)
- MambaQuant: Quantizing the Mamba Family with Variance Aligned Rotation Methods (ICLR 2025 · similarity 0.83)
- Null Space Matters: Range-Null Decomposition for Consistent Multi-Contrast MRI Reconstruction (AAAI 2024 · similarity 0.82)
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