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Underdetermined Blind Identification for $k$-Sparse Component Analysis using RANSAC-based Orthogonal Subspace Search

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Document pages: 5 pages

Abstract: Sparse component analysis is very popular in solving underdetermined blindsource separation (UBSS) problem. Here, we propose a new underdetermined blindidentification (UBI) approach for estimation of the mixing matrix in UBSS.Previous approaches either rely on single dominant component or consider $k leq m-1$ active sources at each time instant, where $m$ is the number ofmixtures, but impose constraint on the level of noise replacing inactivesources. Here, we propose an effective, computationally less complex, and morerobust to noise UBI approach to tackle such restrictions when $k = m-1$ basedon a two-step scenario: (1) estimating the orthogonal complement subspaces ofthe overall space and (2) identifying the mixing vectors. For this purpose, anintegrated algorithm is presented to solve both steps based on Gram-Schmidtprocess and random sample consensus method. Experimental results usingsimulated data show more effectiveness of the proposed method compared with theexisting algorithms.

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