A sparse adaptive filtering using time-varying soft-thresholding techniques

Yukihiro Murakami, Masao Yamagishi, Masahiro Yukawa, Isao Yamada
2010 2010 IEEE International Conference on Acoustics, Speech and Signal Processing  
In this paper, we propose a novel adaptive filtering algorithm based on an iterative use of (i) the proximity operator and (ii) the parallel variable-metric projection. Our time-varying cost function is a weighted sum of squared distances (in a variable-metric sense) plus a possibly nonsmooth penalty term, and the proposed algorithm is derived along the idea of proximal forward-backward splitting in convex analysis. For application to sparse-system identification problems, we employ the
more » ... d) 1 norm as the penalty term, leading to a time-varying soft-thresholding operator. As the simple example of the proposed algorithm, we present the variable-metric affine projection algorithm composed with the time-varying softthresholding operator. Numerical examples demonstrate that the proposed algorithms notably outperform their counterparts without soft-thresholding both in convergence speed and steady-state mismatch, while the extra computational complexity due to the additional soft-thresholding is negligibly low. Index Termssparse adaptive filtering, proximal forwardbackward splitting, soft-thresholding, variable metric, parallel projection
doi:10.1109/icassp.2010.5495870 dblp:conf/icassp/MurakamiYYY10 fatcat:majw2dw3cfaqdb6ciuc4kp3in4