Learned Successive Convex Approximation for Sparse Signal Recovery

Sparse signal recovery using the least absolute shrinkage and selection operator (LASSO) and model-aided deep learning is considered. We propose the Learned SoftThresholding with Exact Line search Algorithm (LSTELA) deep network architecture which is based on unrolling a successive convex approximation algorithm. LSTELA incorporates debiasing through the use of the soft-thresholding with support selection operator and revised step size rules as well as instanceadaptive parameters. In addition, we introduce a novel piecewise differentiable approximation of the soft-thresholding with support selection operator, which allows all model parameters to be learned end-to-end, avoiding a computationally costly gradient-free search. We further propose a lightweight LSTELA variant to improve the computational efficiency. Compared to state-of-the-art model-aided network architectures, the proposed unrolling-based methods achieve a lower MSE in the case of noise-contaminated measurements while exhibiting excellent adaptation capabilities in case of changing data distributions.