Generalized Iterative Thresholding for Sparsity-Aware Online Volterra System Identification

Abstract:
The present paper explores the link between thresholding, one of the key enablers in sparsity-promoting algorithms, and Volterra system identification in the context of time-adaptive or online learning. A connection is established between the recently developed generalized thresholding operator and optimization theory via the concept of proximalmappings which are associated with non-convex penalizing functions. Based on such a variational analytic ground, two iterative thresholding algorithms are provided for the sparsity-cognizant Volterra system identification task: (i) a set theoretic estimation one by using projections onto hyperslabs, and (ii) a Landweber-type one. Numerical experimentation is provided to validate the proposed algorithms with respect to state-ofthe- art, sparsity-aware online learning techniques.