Multivariate Fields of Experts for Convergent Image Reconstruction

TL;DR

This paper presents a new multivariate fields of experts framework for image reconstruction that outperforms univariate models, approaches deep-learning performance, and offers interpretability and theoretical guarantees.

Contribution

Introduction of multivariate fields of experts with structured potential functions for improved, interpretable image priors in inverse problems.

Findings

Outperforms univariate models in various inverse tasks.

Achieves near deep-learning regularizer performance.

Requires fewer parameters and less training data.

Abstract

We introduce the multivariate fields of experts, a new framework for the learning of image priors. Our model generalizes existing fields of experts methods by incorporating multivariate potential functions constructed via Moreau envelopes of the $\ell_\infty$-norm. We demonstrate the effectiveness of our proposal across a range of inverse problems that include image denoising, deblurring, compressed-sensing magnetic-resonance imaging, and computed tomography. The proposed approach outperforms comparable univariate models and achieves performance close to that of deep-learning-based regularizers while being significantly faster, requiring fewer parameters, and being trained on substantially fewer data. In addition, our model retains a high level of interpretability due to its structured design. It is supported by theoretical convergence guarantees which ensure reliability in sensitive reconstruction tasks.