Robust lEarned Shrinkage-Thresholding (REST): Robust unrolling for sparse recover
This addresses robust signal recovery for applications like sensing and imaging, but it is incremental as it builds on existing unrolling techniques.
The paper tackles the problem of robust sparse recovery under forward model mis-specifications by proposing the REST network, which outperforms state-of-the-art methods in compressive sensing and radar imaging with model mismatch.
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.