Weakly-Convex Regularization for Magnetic Resonance Image Denoising

TL;DR

This paper introduces a novel weakly-convex regularization method for MRI denoising that matches state-of-the-art performance while enhancing interpretability, stability, and reducing artifacts.

Contribution

It proposes a constructive approach for designing weakly-convex regularization functions and neural networks with interpretability and convergence guarantees for MRI denoising.

Findings

Performs on par with leading denoisers for diffusion-weighted MRI

Designs interpretable, provably convergent neural networks

Reduces denoising artifacts in brain microstructure imaging

Abstract

Regularization for denoising in magnetic resonance imaging (MRI) is typically achieved using convex regularization functions. Recently, deep learning techniques have been shown to provide superior denoising performance. However, this comes at the price of lack of explainability, interpretability and stability, which are all crucial to MRI. In this work, we present a constructive approach for designing weakly-convex regularization functions for MR image denoising. We show that our technique performs on par with state-of-the-art denoisers for diffusion-weighted MR image denoising. Our technique can be applied to design weakly-convex convolutional neural networks with prototype activation functions that impart interpretability and are provably convergent. We also show that our technique exhibits fewer denoising artifacts by demonstrating its effect on brain microstructure modelling.