Title :
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
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;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2010.2082529
