Adaptive blind separation of underdetermined mixtures based on sparse component analysis

The independence priori is very often used in the conventional blind source separation (BSS). Naturally, independent component analysis (ICA) is also employed to perform BSS very often. However, ICA is difficult to use in some challenging cases, such as underdetermined BSS or blind separation of dependent sources. Recently, sparse component analysis (SCA) has attained much attention because it is theoretically available for underdetermined BSS and even for blind dependent source separation sometimes. However, SCA has not been developed very sufficiently. Up to now, there are only few existing algorithms and they are also not perfect as well in practice. For example, although Lewicki-Sejnowski's natural gradient for SCA is superior to K-mean clustering, it is just an approximation without rigorously theoretical basis. To overcome these problems, a new natural gradient formula is proposed in this paper. This formula is derived directly from the cost function of SCA through matrix theory. Mathematically, it is more rigorous. In addition, a new and robust adaptive BSS algorithm is developed based on the new natural gradient. Simulations illustrate that this natural gradient formula is more robust and reliable than Lewicki-Sejnowski's gradient.