Methods for Source Number Estimation in Underdetermined Blind Sources Separation
Estimate the number of source signals is a necessary prerequisite for underdetermined blind sources separation (UBSS). The accuracy of sources number estimation has influence to the correctness of the sources separation. For this, a new algorithm—Hough-Wi
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Methods for Source Number Estimation in Underdetermined Blind Sources Separation Hui Guo, Yong-qing Fu, Yan Liu and Jian-qiang Wang
Abstract Estimate the number of source signals is a necessary prerequisite for underdetermined blind sources separation (UBSS). The accuracy of sources number estimation has influence to the correctness of the sources separation. For this, a new algorithm—Hough-Windowed is proposed based on the assumption that the source signals are sparse. First, the algorithm constructs straight line equations of the observed signals based on Hough transformation. In order to obtain cluster areas, histogram is cumulated by windowed in transform domain. Then estimate the maximum of every cluster area. The number of different maximum is the number of source signals. Simulation results show the validity and expansibility of the algorithm. At the same time, compared with Potential function, the algorithm reflects the better noise immunity and the lower sparse sensitivity.
Keywords Underdetermined blind sources separation Estimate the number of source signals Sparse representation Hough transformation Histogram Windowed method
H. Guo (&) Y. Fu College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China e-mail: [email protected] Y. Fu e-mail: [email protected] Y. Liu J. Wang EMC Laboratory, Beijing University of Aeronautics and Astronautics, Beijing 100191, China e-mail: [email protected] J. Wang e-mail: [email protected]
W. Lu et al. (eds.), Proceedings of the 2012 International Conference on Information Technology and Software Engineering, Lecture Notes in Electrical Engineering 210, DOI: 10.1007/978-3-642-34528-9_44, Springer-Verlag Berlin Heidelberg 2013
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44.1 Introduction Unknown sources can be recovered only from observations without prior knowledge of mixing channel and source signals by using blind sources separation (BSS). Therefore, the research of it has made great contributions up to now [1–3]. But these research should know the number of source signals firstly. Estimate the number of the source signals is a necessary prerequisite for BSS. The accuracy of the source signals’ number estimations has influence to the correctness of the sources separation. As a case of BSS, underdetermined blind sources separation (UBSS, the number of observation signals is less than that of source signals) is no exception. Because of practical and challenging, UBSS is currently receiving increased interests. The mathematics model of UBSS is XðtÞ ¼ ASðtÞ þ NðtÞ;
t ¼ 1; . . .; T
ð44:1Þ
where XðtÞ ¼ ½x1 ðtÞ; x2 ðtÞ; ; xm ðtÞT is the vector of observed signals. A ¼½a1 ; a2 ; ; an 2 Rmn is the mixture matrix with ai ¼ ½a1i ; a2i ; ; ami T ; i ¼ 1. . .; n: SðtÞ ¼ ½s1 ðtÞ; s2 ðtÞ; . . .; sn ðtÞT , is the vector of source signals. NðtÞ ¼ ½n1 ðtÞ; n2 ðtÞ; ; nm ðtÞT is noise. Generally, we suppose noise doesn’t exist. In this paper considering m is less than n, namely UBSS. Because of
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