Proportionate Adaptive Filters From a Basis Pursuit Perspective - Benesty, Jacob; Paleologu, Constantin; Ciochină, Silviu (IEEE signal processing letters, 2010)
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 ℓ 2 -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 ℓ 1 -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.