Blind source separation for the analysis sparse model

Sparsity of the signal has been shown to be very useful for blind source separation (BSS) problem which aims at recovering unknown sources from their mixtures. In this paper, we propose a novel algorithm based on the analysis sparse constraint of the source over an adaptive analysis dictionary to address BSS problem. This method has an alternating scheme by keeping all but one unknown fixed at a time so that the dictionary, the source, and the mixing matrix are estimated alternatively. In order to make better use of the sparsity constrain, l0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{0}$$\end{document}-norm is utilized directly for a more exact solution instead of its other relaxation, such as lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{\mathrm{p}}$$\end{document}-norm (0<p≤1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<p\le 1$$\end{document}). Numerical experiments show that the proposed method indeed improves the separation performance.