Estimating the Mixing Matrix in Sparse Component Analysis Based on Converting a Multiple Dominant to a Single Dominant Problem

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.