Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms

TL;DR

This paper introduces a method to learn non-convex regularizers with bounded weak-convexity for image reconstruction, resulting in denoisers that outperform traditional methods and ensure convergence in inverse problem solutions.

Contribution

It presents a novel approach to learn weakly convex regularizers with few parameters, providing interpretability, convergence guarantees, and superior performance in image reconstruction tasks.

Findings

Learned denoisers outperform convex regularizers and BM3D.

Regularizers enable provably convergent iterative schemes.

Method generalizes well to CT and MRI reconstructions.

Abstract

We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus. Such regularizers give rise to variational denoisers that minimize a convex energy. They rely on few parameters (less than 15,000) and offer a signal-processing interpretation as they mimic handcrafted sparsity-promoting regularizers. Through numerical experiments, we show that such denoisers outperform convex-regularization methods as well as the popular BM3D denoiser. Additionally, the learned regularizer can be deployed to solve inverse problems with iterative schemes that provably converge. For both CT and MRI reconstruction, the regularizer generalizes well and offers an excellent tradeoff between performance, number of parameters, guarantees, and interpretability when compared to other data-driven approaches.