Iteratively Refined Image Reconstruction with Learned Attentive Regularizers

TL;DR

This paper introduces an interpretable, iterative image reconstruction method combining deep learning with convex regularization, progressively refining image details through learned masks, and demonstrating competitive performance with theoretical guarantees.

Contribution

It presents a novel, interpretable regularization scheme that iteratively refines image reconstruction using learned masks within convex optimization frameworks, with proven convergence properties.

Findings

Matches state-of-the-art performance in inverse problems

Provides theoretical guarantees for convergence

Balances interpretability and effectiveness

Abstract

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze theoretically. In contrast, our scheme is interpretable because it corresponds to the minimization of a series of convex problems. For each problem in the series, a mask is generated based on the previous solution to refine the regularization strength spatially. In this way, the model becomes progressively attentive to the image structure. For the underlying update operator, we prove the existence of a fixed point. As a special case, we investigate a mask generator for which the fixed-point iterations converge to a critical point of an explicit energy functional. In our experiments, we match the performance of state-of-the-art learned variational models for the solution of inverse problems. Additionally, we offer a promising balance between interpretability, theoretical guarantees, reliability, and performance.