Proportionate Adaptive Filters From a Basis Pursuit Perspective

Author

Benesty, Jacob ; Paleologu, Constantin ; Ciochin, Silviu

Author_Institution

INRS-EMT, Univ. of Quebec, Montreal, QC, Canada

Volume

17

Issue

12

fYear

2010

Firstpage

985

Lastpage

988

Abstract

In this letter, we show that the normalized least-mean-square (NLMS) algorithm and the affine projection algorithm (APA) can be decomposed as the sum of two orthogonal vectors. One of these vectors is derived from an ℓ₂-norm optimization problem while the other one is simply a good initialization vector. By replacing this optimization with the basis pursuit, which is based on the ℓ₁-norm optimization, we derive the proportionate NLMS (PNLMS) algorithm and the proportionate APA (PAPA). Many other adaptive filters can be derived following this approach, including new ones.

Keywords

adaptive filters; least mean squares methods; optimisation; NLMS algorithm; affine projection algorithm; basis pursuit perspective; initialization vector; l₁ -norm optimization problem; l₂ -norm optimization problem; normalized least mean square algorithm; orthogonal vectors; proportionate APA; proportionate adaptive filters; Adaptive filters; Convergence; Echo cancellers; Least mean square algorithms; Optimization; Signal processing algorithms; APA; Adaptive filters; NLMS; PAPA; PNLMS; basis pursuit; echo cancellation;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2010.2082529

Filename

5593204