Underdetermined Blind Separation of an Unknown Number of Sources Based on Fourier Transform and Matrix Factorization

This paper presents an approach for underdetermined blind source
separation that can be applied even if the number of sources is unknown. Moreover,
the proposed approach is applicable in the case of separating I+3 sources from I
mixtures without additive noise. This situation is more challenging and suitable to
practical real world problems. Also, the sparsity conditions are not imposed unlike to
those employed by some conventional approaches. Firstly, the number of source
signals are estimated followed by the estimation of the mixing matrix based on the
use of short time Fourier transform and rough-fuzzy clustering. Then, source signals
are normalized and recovered using modified Lin_s projected gradient algorithm with
modified Armijo rule. The 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 conventional approaches.