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.