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Patch2Self2: Self-supervised Denoising on Coresets via Matrix Sketching
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Proposes Patch2Self2, which speeds up and reduces memory for Patch2Self dMRI denoising by solving the self-supervised linear regression on a leverage-score sketched coreset, with RRQR-based sketch size calibration.
Problem
Patch2Self (P2S) self-supervised dMRI denoising is slow and memory-hungry because it regresses over all n voxels of a Casorati matrix, which becomes infeasible for high-resolution, high-dimensional acquisitions.
Approach
Applies randomized matrix sketching (CountSketch, SRFT, leverage-score sampling) to the Casorati matrix to build a small coreset for the J-invariant linear regression, selects the sketch size via RRQR rank estimation, and uses statistical leverage scores to interpret denoising.
Key results
- On simulated dMRI, P2S2 trained on 20K samples (7% of data) matches P2S in RMSE and R2 across SNR 10-30.
- Leverage-score sampling gives slightly lower solution error than CountSketch and outperforms uniform sampling and deterministic top-leverage selection across sketch sizes.
- P2S2 trained on 50K of 61M samples (0.083%) on HCP 7T yields DKI metrics similar to P2S; speedup grows as sketch size shrinks and with data dimensionality.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use leverage-score sampling to construct the coreset | Patch2Self2 · dMRI denoising | denoising performance | Helped |
| Train on a reduced subset using matrix sketching | Patch2Self2 · simulated and real dMRI data | denoising quality | No clear effect |
| Train on a reduced subset using matrix sketching | Patch2Self2 · dMRI denoising | training time | Helped |
| Train on a reduced subset using matrix sketching | Patch2Self2 · dMRI denoising | memory usage | Helped |
| Use randomized leverage-score sampling instead of deterministic selection of the top leverage scores (ablation) | Patch2Self2 · PPMI | denoising performance | Helped |
| Use randomized sketching instead of uniform sampling (ablation) | Patch2Self2 · PPMI | solution approximation error | Helped |
| Use leverage-score sampling instead of CountSketch (ablation) | Patch2Self2 · PPMI | solution approximation error | Helped |
| Use randomized leverage-score sampling instead of SRFT (ablation) | Patch2Self2 · PPMI | solution approximation error | Mixed |
| Increase sketch size (ablation) | Patch2Self2 · PPMI | variance of solution approximation error | Helped |
| Use P2S2 rather than P2S | Patch2Self2 · simulated dMRI data | RMSE | No clear effect |
| Use P2S2 rather than P2S | Patch2Self2 · simulated dMRI data | R^2 | No clear effect |
| Use P2S2 rather than noisy input | Patch2Self2 · simulated dMRI data | denoising efficiency | Helped |
Surprising findings
- Deterministic selection of the top leverage-score rows performs worse than randomized leverage-score sampling, attributed to the bimodal distribution of randomly sampled scores.
Limitations
- Introduces a sketch-size hyperparameter that must be calibrated, with RRQR cost O(d^3 log d) in worst case.
- Evaluation is mostly qualitative on real data, with downstream metrics compared only against P2S rather than ground truth.
Experimental setup
Datasets: HCP 7T dMRI PPMI dMRI Stanford HARDI Porcine cardiac data simulated dMRI
Benchmarks: HCP 7T dMRI PPMI dMRI Stanford HARDI simulated dMRI (SNR 10-30)
Metrics: MSE R2 relative error of solution speedup wall-clock time radial and mean kurtosis fiber-to-bundle coherence
Baselines: Patch2Self uniform sampling CountSketch SRFT
Builds on: Patch2Self Noise2Self Noise2Noise sketch-and-solve regression
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