Estimating the mixing matrix in underdetermined Spare Component Analysis (SCA) using consecutive Independent Component Analysis (ICA)
Résumé
One of the major problems in underdetermined Sparse Component Analysis (SCA) is the appropriate estimation of the mixing matrix, A, in the linear model x(t) = As(t), especially where more than one source is active at each instant of time (It is called 'multiple dominant problem'). Most of the previous algorithms were restricted to single dominant problem in which it is assumed that at each instant, there is at most one single dominant component. Moreover, because of high computational load, all present methods for multiple dominant problem are practical only for small scale cases (By 'small scale' we mean that the average number of active sources at each instant, k, is less than 5). In this paper, we propose a new method for estimating the mixing matrix, A for the large scale multiple dominant problem in SCA. Our main idea is to convert the underdetermined SCA problem into a series of determined problems, which can be solved by well-known methods like ICA. To do this, we combine both sparsity and independence assumptions to estimate the mixing matrix. Our method can solve high dimension problems in which k can be relatively large (about 8).
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