SpringerLink - Journal Article

Adaptive blind separation of underdetermined mixtures based on sparse component analysis

ZuYuan Yang¹, ZhaoShui He¹, ShengLi Xie¹ and YuLi Fu¹

(1)	School of Electronics & Information Engineering, South China University of Technology, Guangzhou, 510640, China

Received: 11 November 2006 Accepted: 11 September 2007 Published online: 27 March 2008

Abstract 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.

Keywords underdetermined mixtures - blind source separation (BSS) - dependent sources - sparse component analysis (SCA) - sparse representation - independent component analysis (ICA) - natural gradient

Supported by the National Natural Science Foundation of China (Grant Nos. 60505005, 60674033, 60774094 and U0635001), the Natural Science Fund of Guangdong Province, China (Grant Nos. 05103553 and 05006508), the Postdoctoral Science Foundation for Innovation from South China University of Technology, and China Postdoctoral Science Foundation (Grant No. 20070410237)

ShengLi Xie
Email: adshlxie@scut.edu.cn

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