Cholesky factors based wavelet transform domain LMF algorithm

Abstract

This paper presents a new wavelet transform domain least mean fourth (LMF) algorithm. The algorithm exploits the special sparse structure of the wavelet transform of wide classes of correlation matrices and their Cholesky factors in order to compute a whitening transformation of the input data in the wavelet domain and minimize computational complexity. This method explicitly computes a sparse estimate of the wavelet domain correlation matrix of the input process. It then computes the Cholesky factor of that matrix and uses its inverse to whiten the input. The proposed algorithm has faster convergence rate than that of wavelet transform domain least mean square (LMS) algorithm.