Underdetermined Blind Separation of Mixtures of an Unknown Number of Sources with Additive White and Pink Noises

In this paper we propose an approach for underdetermined blind separation in the case of additive Gaussian white noise and pink noise in addition to the most challenging case where the number of source signals is unknown. In addition to that, the proposed approach is applicable in the case of separating I + 3 source signals from I mixtures with an unknown number of source signals and the mixtures have additive two kinds of noises. This situation is more challenging and also more suitable to practical real world problems. Moreover, unlike to some traditional approaches, the sparsity conditions are not imposed. Firstly, the number of source signals is approximated and estimated using multiple source detection, followed by an algorithm for estimating the mixing matrix based on combining short time Fourier transform and rough-fuzzy clustering. Then, the mixed signals are normalized and the source signals are recovered using multi-layer modified Gradient descent Local Hierarchical Alternating Least Squares Algorithm exploiting the number of source signals estimated, and the mixing matrix obtained as an input and initialized by multiplicative algorithm for matrix factorization based on alpha divergence. The computer simulation results show that the proposed approach can separate I + 3 source signals from I mixed signals, and it has superior evaluation performance compared to some traditional approaches in recent references.