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

Sparse component analysis is very popular in solving underdetermined blind source separation (UBSS) problem. Here, we propose a new underdetermined blind identification (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 of mixtures, but impose constraint on the level of noise replacing inactive sources. Here, we propose an effective, computationally less complex, and more robust to noise UBI approach to tackle such restrictions when $k = m-1$ based on a two-step scenario: (1) estimating the orthogonal complement subspaces of the overall space and (2) identifying the mixing vectors. For this purpose, an integrated algorithm is presented to solve both steps based on Gram-Schmidt process and random sample consensus method. Experimental results using simulated data show more effectiveness of the proposed method compared with the existing algorithms.