Sparse approximation (also known as compressive sensing) is an active research direction in signal processing. The classical approach is based on convex relaxation: replacement the sparsity constraint with a constraint on the ell-1 norm (sum of the absolute values). There exist fast and robust methods for solving ell-1 regularized approximation problems. This project is inspired by a recent result on the link between sparsity and matrix low-rank approximation/completion (see, http://homepages.vub.ac.be/~imarkovs/publications/ica18b.pdf). Methods and software for this latter approach are available from http://slra.github.io.
The goal of the project is to implement and test on simulated and real data examples the ell-1 norm regularization and low-rank approximation methods.