Blind Separation of Instantaneous Mixtures of Independent/Dependent Sources

Blind Source Separation (BSS) has always been an active research field within the signal processing community; it is used to reconstruct primary source signals from their observed mixtures. Independent Component Analysis has been and is still used to solve the BSS problem; however, it is based on the mutual independence of the original source signals. In this paper, we propose to use Copulas to model the dependency structure between these signals, enabling the separation of dependent source components; we also deploy α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-divergence as our cost function to minimize, considering its superiority to handle noisy data as well as its ability to converge faster. We test our approach for various values of alpha and give a comparative study between the proposed methodology and other existing methods; this approach exhibited a higher quality performance and accuracy, especially when the value of α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} is equal to 12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{2}$$\end{document}, which is equivalent to the Hellinger divergence.