The independence priori is very often used in the conventional blind source sepa-ration (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 theo- retically 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 theo- retical basis. To overcome these problems, a new natural gradient formula is pro- posed 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.
Recently,sparse component analysis (SCA) has become a hot spot in BSS re-search. Instead of independent component analysis (ICA),SCA can be used to solve underdetermined mixture efficiently. Two-step approach (TSA) is one of the typical methods to solve SCA based BSS problems. It estimates the mixing matrix before the separation of the sources. K-means clustering is often used to estimate the mixing matrix. It relies on the prior knowledge of the source number strongly. However,the estimation of the source number is an obstacle. In this paper,a fuzzy clustering method is proposed to estimate the source number and mixing matrix simultaneously. After that,the sources are recovered by the shortest path method (SPM). Simulations show the availability and robustness of the proposed method.
