Estimating the mixing matrix in sparse component analysis based on converting a multiple dominant to a single dominant problem

Authors:
Nima Noorshams;Massoud Babaie-Zadeh;Christian Jutten
Affiliations:
Electrical Engineering Department, Advanced Communications Research Institute, Sharif University of Technology, Tehran, Iran;Electrical Engineering Department, Advanced Communications Research Institute, Sharif University of Technology, Tehran, Iran;GIPSA-lab, Department of Images and Signals, National Polytechnic Institute of Grenoble, France
Venue:
ICA'07 Proceedings of the 7th international conference on Independent component analysis and signal separation
Year:
2007

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Abstract

We propose a new method for estimating the mixing matrix, A, in the linear model x(t) = As(t), t = 1, ..., T, for the problem of underdetermined Sparse Component Analysis (SCA). Contrary to most previous algorithms, there can be more than one dominant source at each instant (we call it a "multiple dominant" problem). The main idea is to convert the multiple dominant problem to a series of single dominant problems, which may be solved by well-known methods. Each of these single dominant problems results in the determination of some columns of A. This results in a huge decrease in computations, which lets us to solve higher dimension problems that were not possible before.