Sparsity-Aware Data-Selective Adaptive Filters

Abstract

We propose two adaptive filtering algorithms that combine sparsity-promoting schemes with data-selection mechanisms. Sparsity is promoted via some well-known nonconvex approximations to the l <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> norm in order to increase convergence speed of the algorithms when dealing with sparse/compressible signals. These approximations circumvent some difficulties of working with the l <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> norm, thus allowing the development of online data-selective algorithms. Data selection is implemented based on set-membership filtering, which yields robustness against noise and reduced computational burden. The proposed algorithms are analyzed in order to set properly their parameters to guarantee stability. In addition, we characterize their updating processes from a geometrical viewpoint. Simulation results show that the proposed algorithms outperform the state-of-the-art algorithms designed to exploit sparsity.