We formulate conditions under which we can solve precisely the Blind Source Separation problem (BSS) in the under-determined case (less sensors than sources), up to permutation and scaling of sources. Under these conditions, which include information about sparseness of the sources (and hence we call the problem sparse component analysis (SCA)), we can 1) identify the mixing matrix uniquely (up to scaling and permutation) and 2) recover uniquely the original sources. We present a new algorithm for estimation of the mixing matrix, as well as an algorithm for SCA (estimation of sparse sources), which improves the standard basis pursuit method of S. Chen, D. Donoho and M. Sounders (when the mixing matrix is known or correctly estimated). Our methods are illustrated with examples.
|Journal||Proceedings - IEEE International Symposium on Circuits and Systems|
|Publication status||Published - 2004|
|Event||2004 IEEE International Symposium on Cirquits and Systems - Proceedings - Vancouver, BC, Canada|
Duration: 23 May 2004 → 26 May 2004