Under-Determined Blind Source Separation

The Under-determined Blind Source Separation problem aims at estimating N source signals, with only a given set of M known mixtures, where M < N. The problem is solved by a two-stage approach. The rst stage is the estimation of the unknown mixing matrix. The contributions made unravel a more precise and accurate tool which directly relates to the initialization of the clustering algorithm. Di erent schemes such as segmentation, correlation and least square curve tting are used to take advantage of the sparsity of the sources. A signi cant addition involves applying linear transforms to produce a higher sparse domain. Further, the second stage is the sparse source recovery using a Matching Pursuit algorithm. The contributions involve a Matching Pursuit algorithm with di