Patch2Self denoising of Diffusion MRI with Self-Supervision and Matrix Sketching

Abstract

Diffusion-weighted magnetic resonance imaging (DWI) is the only noninvasive method for quantifying microstructure and reconstructing white-matter pathways in the living human brain. Fluctuations from multiple sources create significant additive noise in DWI data which must be suppressed before subsequent microstructure analysis. We introduce a self-supervised learning method for denoising DWI data, Patch2Self (P2S), 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, P2S can separate structure from noise without requiring an explicit model for either. The setup of P2S however can be 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. We exploit the redundancy imposed by P2S to alleviate its performance issues and inspect regions that influence the noise disproportionately. Specifically we introduce P2S-sketch, which makes a two-fold contribution: \textit{(1)} P2S-sketch uses matrix sketching to perform self-supervised denoising. By solving a sub-problem on a smaller sub-space, so called, \textit{coreset}, we show how P2S can yield a significant speedup in training time while using less memory. \textit{(2)} We show how the so-called statistical leverage scores can be used to \textit{interpret} the denoising of dMRI data, a process that was traditionally treated as a black-box. Our experiments conducted on simulated and real data clearly demonstrate that P2S via matrix sketching (P2S-sketch) does not lead to any loss in denoising quality, while yielding significant speedup and improved memory usage by training on a smaller fraction of the data. With thorough comparisons on real and simulated data, we show that Patch2Self outperforms the current state-of-the-art methods for DWI denoising both in terms of visual conspicuity and downstream modeling tasks. We demonstrate the effectiveness of our approach via multiple quantitative metrics such as fiber bundle coherence, $R^2$ via cross-validation on model fitting, mean absolute error of DTI residuals across a cohort of sixty subjects.

NUQ: A Noise Metric for Diffusion MRI via Uncertainty Discrepancy Quantification

“…2A where different denoisers are compared via RTOP and FA. Multi-ONLM is known to cause spatial smoothing whereas MPPCA and Patch2Self do not [6] (see supplement for a comparison). One can see qualitatively (via NUQ quality maps) and quantitatively (via NUQ scores) that for the case of RTOP on the CFIN data and FA on the LA5c data, despite smoothing the signal, Multi-ONLM has a higher uncertainty as compared to MPPCA and Patch2Self.…”

“…The model is then used to infer the underlying (sub-voxel resolution) tissue microstructure. Due to the inherent noise in the acquired signal, this ill-posed inverse problem leads to fitting degeneracies and unreliable estimates of the underlying cellular organization [6]. These errors propagate and amplify the uncertainty in downstream tasks such as tractography and group-level analyses.…”

“…We consider the first case of denoisers that deal with magnitude data. These can be further categorized based on their underlying assumptions; popular and successful ones include low-rank approximations (Marchenko Pastur PCA) [27], self-similarity (Multi-resolution Optimized Non-Local Means (Multi-ONLM)) [17] and statistical independence (Patch2Self) [6]. To demonstrate the utility of the proposed noise metric-Noise Uncertainty Quantification (NUQ)-we show that it captures subtle details across this range of denoisers as well as with data acquired with different schemes.…”

Self-Supervised Bulk Motion Artifact Removal in Optical Coherence Tomography Angiography

“…More and more unsupervised learning based denoising methods [1,6,10,13] have been proposed and achieves promising performance. However, these approaches are not intended to correct structural noise.…”

Improved reproducibility of diffusion kurtosis imaging using regularized non-linear optimization informed by artificial neural networks

“…Dipy (Garyfallidis et al, 2014) was used to denoise the raw images using patch2self (Fadnavis et al, 2020), a self-supervised algorithm that learns to separate signal from noise without model assumptions using oversampled data. MRtrix3 (Tournier et al, 2019) was used to reduce Gibbs ringing artefacts with a sub-voxel shift algorithm (Kellner et al, 2016) and to correct for distortions induced by motion, susceptibility, and eddy currents using FSL's topup and eddy (Andersson and Sotiropoulos, 2016;Smith et al, 2004).…”