Underdetermined instantaneous blind source separation of sparse signals with temporal structure using the state-space model

In this work, we exploit, in addition to sparseness, the temporal structure of the source signals to address the problem of underdetermined blind source separation. To achieve good separation performance and reduction of artifacts, a two-stage algorithm is proposed. In the first stage, the auto-regressive (AR) coefficients of the source signals are estimated using partially separated sources that have been derived from conventional sparseness-based algorithm. In the second stage, the AR model is combined with the mixing equation to form a state-space model. This model is subsequently solved using the Kalman filter in order to obtain the refined source estimate. Simulation results show the effectiveness of proposed sparseness-based AR-Kalman (SPARK) algorithm compared to the conventional sparseness-based algorithms.