Underdetermined blind source separation in a time-varying environment
Luis Vielva, Deniz Erdoğmuş, C. Pantaleón, Ignacio Santamarı́a, José Antonio Martín Pereda, José Carlos Príncipe · IEEE International Conference on Acoustics Speech and Signal Processing · 2002
The problem of estimating n source signals from m measurements that are an unknown mixture of the sources is known as blind source separation. In the underdetermined —less measurements than sources— linear case, the solution process can be conveniently divided in three stages: represent the signals in a sparse domain, find the mixing matrix, and estimate the sources. In this paper we adhere to that approach and parametrize the performance of these stages as a function of the sparsity of the signals. To find the mixing matrix and track its variations in the dynamic case a nonparametric maximum-likelihood approach based on Parzen windowing is presented. To invert the underdetermined linear problem we present an estimator that chooses the “best” demixing matrix in a sample by sample basis by using some previous knowledge of the statistics of the sources. The results are validated by Montecarlo simulations.