Group sparse RLS algorithms. (English) Zbl 1334.93188

Eksioglu, Ender M.

Int. J. Adapt. Control Signal Process. 28, No. 12, 1398-1412 (2014).

Summary: Group sparsity is one of the important signal priors for regularization of inverse problems. Sparsity with group structure is encountered in numerous applications. However, despite the abundance of sparsity-based adaptive algorithms, attempts at group sparse adaptive methods are very scarce. In this paper, we introduce novel recursive least squares (RLS) adaptive algorithms regularized via penalty functions, which promote group sparsity. We present a new analytic approximation for \(\ell_{p,0}\) norm to utilize it as a group sparse regularizer. Simulation results confirm the improved performance of the new group sparse algorithms over regular and sparse RLS algorithms when group sparse structure is present.

MSC:

93E24	Least squares and related methods for stochastic control systems
93E11	Filtering in stochastic control theory
93C40	Adaptive control/observation systems
93B30	System identification

Keywords:

adaptive filter; RLS; sparsity; group sparsity; block structure; mixed norm