Patch2Self2: Self-supervised Denoising on Coresets via Matrix Sketching

Diffusion MRI (dMRI) non-invasively maps brain white matter, yet necessitates denoising due to low signal-to-noise ratios. Patch2Self (P2S), employing self-supervised techniques and regression on a Casorati matrix, effectively denoises dMRI images and has become the new de-facto standard in this field. P2S however is resource intensive, both in terms of running time and memory usage, as it uses all voxels ($n$) from all-but-one held-in volumes ($d-1$) to learn a linear mapping $\Phi : \mathbb{R}^{n \times (d-1)} \mapsto \mathbb{R}^{n}$ for denoising the held-out volume. The increasing size and dimensionality of higher resolution dMRI acquisitions can make P2S infeasible for large-scale analyses. This work exploits the redundancy imposed by P2S to alleviate its performance issues and inspect regions that influence the noise disproportionately. Specifically, this study makes a three-fold contribution: (1) We present Patch2Self2 (P2S2), a method that uses matrix sketching to perform self-supervised denoising. By solving a sub-problem on a smaller sub-space, so called, coreset, we show how P2S2 can yield a significant speedup in training time while using less memory. (2) We present a theoretical analysis of P2S2, focusing on determining the optimal sketch size through rank estimation, a key step in achieving a balance between denoising accuracy and computational efficiency. (3) We show how the so-called statistical leverage scores can be used to interpret the denoising of dMRI data, a process that was traditionally treated as a black-box. Experimental results on both simulated and real data affirm that P2S2 maintains denoising quality while significantly enhancing speed and memory efficiency, achieved by training on a reduced data subset.