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Time-Embedded Algorithm Unrolling for Computational MRI
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Proposes time-embedded algorithm unrolling for MRI reconstruction, where the proximal operator, data-fidelity weight and Onsager correction are made iteration-dependent via time embeddings (FiLM), sharing one network across unrolls.
Problem
Algorithm unrolling for regularized least-squares MRI reconstruction must choose between a shared proximal network across unrolls (artifacts/blurring) and unshared networks (many parameters, overfitting in limited-data settings).
Approach
Inspired by VAMP's iteration-dependent proximal operator and Onsager correction and by time-embedding in diffusion models, a single proximal network is conditioned on the unroll index via sinusoidal time embeddings with FiLM, and the data-fidelity weight and Onsager scalars are learned per iteration.
Key results
- On coronal PD at R=8 with ResNet, the time-embedded method (10 unrolls) reaches 36.87 dB PSNR vs 36.46 dB for shared VSQP and 36.72 dB for shared ADMM.
- With only 5 unrolls, the method is comparable to shared baselines with 10 unrolls in most cases, roughly halving network computation and inference time.
- Time-embedding extended to VSQP and ADMM improves PSNR across all acceleration rates.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use time-embedded unrolling instead of shared-regularizer unrolling | MRI reconstruction with ResNet proximal operators · Coronal PD, R=4 | PSNR: 41.27 -> 41.43 | Helped |
| Use time-embedded unrolling instead of shared-regularizer unrolling | MRI reconstruction with ResNet proximal operators · Coronal PD-FS, R=6 | PSNR: 34.53 -> 34.59 | Helped |
| Use time-embedded unrolling instead of shared-regularizer unrolling | MRI reconstruction with ResNet proximal operators · Axial T2, R=4 | PSNR: 36.81 -> 36.81 | No clear effect |
| Use 10 instead of 5 unrolls (ablation) | Time-embedded unrolling, U-Net proximal operator · Coronal PD, R=4 | PSNR: 40.94 -> 40.99 | No clear effect |
| Increase the number of unrolls from 5 to 15 (ablation) | Time-embedded unrolling, ResNet proximal operator · Coronal PD, R=8 | PSNR: 36.76 -> 37.09 | Helped |
| Train unshared ADMM from scratch rather than fine-tuning from the shared model (ablation) | ADMM unrolling, U-Net proximal operator · Coronal PD, R=4 | PSNR: 40.96 -> 40.51 | Hurt |
| Increase the number of training parameters in the shared and unshared baselines (ablation) | MRI reconstruction models · Coronal PD, R=4 | performance | Mixed |
| Change time-embedding hyperparameters (ablation) | Time-embedded U-Net · Coronal PD-FS, R=6 | performance | Mixed |
Surprising findings
- Unshared proximal networks often perform worse than shared ones in the limited-data setting, attributed to overfitting.
- Fine-tuning unshared networks from shared pretrained weights improves PSNR but still leaves residual artifacts.
Limitations
- Experiments limited to 300 training slices per dataset; performance gap to unshared models may narrow with more data.
- Did not beat baselines on every SSIM entry; some cases fall outside top-two.
- Evaluated only on uniform (equispaced) undersampling in the main experiments.
Experimental setup
Datasets: NYU fastMRI knee (coronal PD, PD-FS) NYU fastMRI brain (axial T2) fastMRI+
Benchmarks: fastMRI coronal PD fastMRI coronal PD-FS fastMRI axial T2
Metrics: PSNR SSIM
Baselines: VSQP shared VSQP unshared ADMM shared ADMM unshared DDS
Builds on: VAMP approximate message passing ADMM unrolling VSQP unrolling ADM diffusion U-Net FiLM
Closest papers by meaning
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- A Unified Model for Compressed Sensing MRI Across Undersampling Patterns (CVPR 2025 · similarity 0.85)
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- What's in a Prior? Learned Proximal Networks for Inverse Problems (ICLR 2024 · similarity 0.85)
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