  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.
