Generalized Thresholding Sparsity-Aware Online Learning in a Union of Subspaces

This paper studies a non-convexly constrained, sparse inverse problem in time-varying environments from a set theoretic estimation perspective. A new theory is developed that allows for the incorporation, in a unifying way, of different thresholding rules to promote sparsity, that may be even related to non-convex penalty functions. The resulted generalized thresholding operator is embodied in an efficient online, sparsity-aware learning scheme. The algorithm is of low computational complexity exhibiting a linear dependence on the number of free parameters. A convergence analysis of the proposed algorithm is conducted, and extensive experiments are also exhibited in order to validate the novel methodology. Index Terms Inverse problems, sparsity, non-convex, partially quasi-nonexpansive mappings, online signal recovery.