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 de-noises dMRI images and has become the new de-facto stan-dard 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 ϕ: R$n$x (d-l) →R n for denoising the held-out volume. The increasing size and dimensionality of higher resolution dMRI acquisitions can make P2S infeasi-ble for large-scale analyses. This work exploits the redun-dancy imposed by P2S to alleviate its performance issues and inspect regions that influence the noise disproportion-ately. 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 com-putational efficiency. (3) We show how the so-called statis-tical 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 sig-nificantly enhancing speed and memory efficiency, achieved by training on a reduced data subset.

Diffusion-weighted magnetic resonance imaging (DWI) is the only non-invasive method for quantifying microstructure and reconstructing white-matter pathways in the living human brain. Fluctuations from multiple sources create significant noise in DWI data which must be suppressed before subsequent microstructure analysis. We introduce a self-supervised learning method for denoising DWI data, Patch2Self, which uses the entire volume to learn a full-rank locally linear denoiser for that volume. By taking advantage of the oversampled q-space of DWI data, Patch2Self can separate structure from noise without requiring an explicit model for either. We demonstrate the effectiveness of Patch2Self via quantitative and qualitative improvements in microstructure modeling, tracking (via fiber bundle coherency) and model estimation relative to other unsupervised methods on real and simulated data.