Robust lEarned Shrinkage-Thresholding (REST): Robust unrolling for sparse recover

TL;DR

This paper introduces REST, a robust neural network architecture based on algorithm unfolding, designed to accurately recover sparse signals despite uncertainties and mismatches in the measurement model.

Contribution

The paper proposes REST, a novel robust deep unfolding network that incorporates normalization to handle model mismatch in sparse recovery tasks.

Findings

REST outperforms existing algorithms in compressive sensing.

REST demonstrates superior robustness in radar imaging with model mismatch.

The architecture effectively manages sample-wise model uncertainties.

Abstract

In this paper, we consider deep neural networks for solving inverse problems that are robust to forward model mis-specifications. Specifically, we treat sensing problems with model mismatch where one wishes to recover a sparse high-dimensional vector from low-dimensional observations subject to uncertainty in the measurement operator. We then design a new robust deep neural network architecture by applying algorithm unfolding techniques to a robust version of the underlying recovery problem. Our proposed network - named Robust lEarned Shrinkage-Thresholding (REST) - exhibits an additional normalization processing compared to Learned Iterative Shrinkage-Thresholding Algorithm (LISTA), leading to reliable recovery of the signal under sample-wise varying model mismatch. The proposed REST network is shown to outperform state-of-the-art model-based and data-driven algorithms in both compressive sensing and radar imaging problems wherein model mismatch is taken into consideration.