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Null Space Matters: Range-Null Decomposition for Consistent Multi-Contrast MRI Reconstruction
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Proposes RNU, a range-null decomposition-assisted deep unfolding network (ISTA-based) with a correlation decoupling block that fuses isotropic (low-frequency, transformer-based) features from a reference contrast while keeping anisotropic (high-frequency, CNN-based multi-expert) features, for consistent multi-contrast MRI reconstruction.
Problem
Multi-contrast MRI reconstruction from undersampled k-space suffers from data inconsistency and poor anatomical structure, and naively using reference contrast features adds inter-domain variation rather than useful information.
Approach
Decompose the image into range and null space via the pseudo-inverse of the undersampling operator, keep the range component fixed from measured k-space and refine only the null-space component in the proximal step; additionally decouple features into frequency-based isotropic (shared, Fourier-modulated transformer encoder) and anisotropic (modality-specific, multi-expert CNN) parts and fuse only
Key results
- On IXI at x4 random mask, RNU (reported as RNECD in Table 1) reaches 43.323 dB PSNR, versus 38.997 dB for GAHQS and 39.037 dB for DuDoCAF.
- On fastMRI x8 random mask, RNU reaches 28.379 dB PSNR / 0.795 SSIM, against 27.723 dB for the best listed baseline in that column.
- Range-null decomposition beats the plain ISTA counterpart at every stage count in ablation (Fig. 7), and LKFFN improves over FFN by 0.595 dB PSNR in the ablation (Table 3).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use range-null decomposition in the fidelity update (ablation) | ISTA-based RNU · IXI, Gaussian mask, ×4 acceleration | PSNR | Helped |
| Replace global MSA with FMM attention (ablation) | RNU · IXI, ×4 random acceleration | PSNR: 38.199 -> 38.287 | Helped |
| Replace local W-MSA with FMM attention (ablation) | RNU · IXI, ×4 random acceleration | PSNR: 37.595 -> 38.287 | Helped |
| Use LKFFN instead of FFN (ablation) | RNU · IXI, ×4 random acceleration | PSNR: 38.579 -> 39.174 | Helped |
| Use LKFFN instead of ConvFFN (ablation) | RNU · IXI, ×4 random acceleration | PSNR: 38.733 -> 39.174 | Helped |
| Use LKFFN instead of GDFN (ablation) | RNU · IXI, ×4 random acceleration | PSNR: 38.928 -> 39.174 | Helped |
| Add reference-modality information through modality decoupling (ablation) | RNU · IXI, ×4 random acceleration | PSNR: 35.198 -> 39.174 | Helped |
| Replace conventional multi-modality fusion with modality decoupling (ablation) | RNU · IXI, ×4 random acceleration | PSNR: 37.747 -> 39.174 | Helped |
| Use RNU instead of the strongest reported baseline | MRI reconstruction · IXI, ×4 random mask | PSNR: +4.33 | Helped |
| Use RNU instead of the strongest reported baseline | MRI reconstruction · IXI, ×4 random mask | PSNR: +4.36 | Helped |
Limitations
- Evaluated only on two datasets (IXI and fastMRI knee) with a single unfolding backbone (ISTA).
- Reported numbers are inconsistent in naming (RNU vs RNECD) and some Table 1 baseline values appear to be mismatched, weakening comparison clarity.
Experimental setup
Datasets: IXI fastMRI
Benchmarks: IXI fastMRI
Metrics: PSNR SSIM
Baselines: Unet MICCAN MDUNet DuDorNet MDDAN DuDoCAF GAHQS
Builds on: ISTA-Net ISTA Transformer DuDoRNet
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