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Moner: Motion Correction in Undersampled Radial MRI with Unsupervised Neural Representation
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Proposes Moner, an unsupervised implicit-neural-representation method that jointly reconstructs and motion-corrects undersampled radial MRI from rigid-motion-corrupted k-space without any training data.
Problem
Motion correction and reconstruction of undersampled, rigid motion-corrupted radial MRI; supervised and pretrained-prior methods need large MRI datasets and generalize poorly out-of-domain.
Approach
Combines an implicit neural representation (hash-encoded MLP) with a learnable quasi-static rigid motion model per spoke, reformulates radial MRI recovery as back-projection via the Fourier-slice theorem to avoid high dynamic range k-space losses, and uses a coarse-to-fine hash encoding schedule that first captures low-frequency structure for motion estimation.
Key results
- On fastMRI, Moner's PSNR is comparable to Score-MoCo (e.g., 32.64 vs 33.94 dB at AF 2x, ±2), but on out-of-domain MoDL it reaches about 33-35 dB where Score-MoCo degrades (e.g., 33.50 vs 28.45 dB at AF 4x, ±2).
- Moner reconstructs more than 5x and 6x faster than Score-MoCo on fastMRI (single RTX 4070 Ti).
- Moner's rotation and shift motion-error metrics are far lower than TV and Score-MoCo at AF 4x (e.g., sigma_tau 0.060 vs 0.312 at ±2 on fastMRI).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Moner instead of Score-MoCo for reconstruction | fastMRI · AF 2×, MR ±5 | PSNR: 33.64±2.22 -> 32.62±2.61 | Hurt |
| Use Moner instead of Score-MoCo for reconstruction | MoDL · AF 4×, MR ±5 | PSNR: 30.09±2.55 -> 33.24±0.88 | Helped |
| Add the quasi-static motion model (ablation) | Moner · fastMRI, AF 2×, MR ±5 | PSNR: over 10 dB | Helped |
| Add the quasi-static motion model (ablation) | Moner · fastMRI, AF 2×, MR ±5 | SSIM: 0.3 | Helped |
| Use the projection-based forward model instead of NuFFT (ablation) | Moner · fastMRI, AF 2×, MR ±5 | MRI reconstruction quality | Helped |
| Use coarse-to-fine hash encoding instead of naive fine hash encoding (ablation) | Moner · fastMRI, AF 2×, MR ±5 | motion estimation accuracy | Helped |
| Use coarse-to-fine hash encoding instead of naive coarse hash encoding (L=6) (ablation) | Moner · fastMRI, AF 2×, MR ±5 | image reconstruction quality | Helped |
Surprising findings
- Score-MoCo, despite being SOTA in-domain, falls below the TV baseline on the out-of-domain MoDL dataset at AF 4x.
Limitations
- Limited to 2D radial MRI; 3D extension is only preliminary.
- Quasi-static rigid motion model cannot handle intra-frame, non-rigid, or spin-history effects.
- Hyper-parameters were tuned on 5 fastMRI training samples; per-case optimization.
Experimental setup
Datasets: fastMRI MoDL
Benchmarks: fastMRI MoDL
Metrics: PSNR SSIM sigma_theta sigma_tau (motion parameter std of absolute errors)
Baselines: NuIFFT TV DRN-DCMB Score-MoCo
Builds on: Score-MoCo Instant-NGP hash encoding Fourier-slice theorem quasi-static motion model
Closest papers by meaning
- MotionTTT: 2D Test-Time-Training Motion Estimation for 3D Motion Corrected MRI (NeurIPS 2024 · similarity 0.85)
- A Unified Model for Compressed Sensing MRI Across Undersampling Patterns (CVPR 2025 · similarity 0.84)
- Efficient Noise Calculation in Deep Learning-based MRI Reconstructions (ICML 2025 · similarity 0.83)
- Autoregressive Image Diffusion: Generation of Image Sequence and Application in MRI (NeurIPS 2024 · similarity 0.83)
- Progressive Divide-and-Conquer via Subsampling Decomposition for Accelerated MRI (CVPR 2024 · similarity 0.83)
- D2SA: Dual-Stage Distribution and Slice Adaptation for Efficient Test-Time Adaptation in MRI Reconstruction (NeurIPS 2025 · similarity 0.83)
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