REST: Robust learned shrinkage-thresholding network taming inverse problems with model mismatch

We consider compressive 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. In particular, we 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 lErned Shrinkage-Thresholding (REST) – exhibits additional features including enlarged number of parameters and normalization processing compared to state-of-the-art deep architecture Learned Iterative Shrinkage-Thresholding Algorithm (LISTA), leading to the reliable recovery of the signal under sample-wise varying model mismatch. Our proposed network is also shown to outperform LISTA in compressive sensing problems under sample-wise varying model mismatch.