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.