Orthogonal segmented model for underdetermined blind identification and separation of sources with sparse events

In this paper, a novel tensor factorization method based on k_a-SCA (called k-SCA in [1]) approach is developed to solve the underdetermined blind source separation (UBSS) and especially underdetermined blind identification (UBI) problems where k_a sources are active in each signal segment. Similar to k_a-SCA methods we assume our k_a is equal to, or less than, the number of sensors minus one when sources are mixed instantaneously. This approach improves the general upper bound for maximum possible number of sources in the second order underdetermind blind identification problem suggested by well known tensor based methods. Alternating constrained optimization approaches are developed to estimate the mixing model and the rank deficient segments. Also this method provides sub-optimum solutions to the UBSS problem. The method is applied to mixtures of synthetic and real signals of sparse events such as instantaneously mixed speech signals. The obtained results show a marked improvement in separability (e.g. it can be used for blind identification and separation of up to 10 speech sources out of 3 sensors) and channel identification compared with other well-established approaches.