Blind source separation with nonlinear autocorrelation and non-Gaussianity

Authors:
Zhenwei Shi;Zhiguo Jiang;Fugen Zhou;Jihao Yin
Affiliations:
Image Processing Center, School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100083, PR China;Image Processing Center, School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100083, PR China;Image Processing Center, School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100083, PR China;Image Processing Center, School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100083, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

Blind source separation (BSS) is a problem that is often encountered in many applications, such as biomedical signal processing and analysis, speech and image processing, wireless telecommunication systems, data mining, sonar, radar enhancement, etc. One often solves the BSS problem by using the statistical properties of original sources, e.g., non-Gaussianity or time-structure information. Nevertheless, real-life mixtures are likely to contain both non-Gaussianity and time-structure information sources, rendering the algorithms using only one statistical property fail. In this paper, we address the BSS problem when source signals have non-Gaussianity and temporal structure with nonlinear autocorrelation. Based on the two statistical characteristics of sources, we develop an objective function. Maximizing the objective function, we propose a gradient ascent source separation algorithm. Furthermore, We give some mathematical properties for the algorithm. Computer simulations for sources with square temporal autocorrelation and non-Gaussianity illustrate the efficiency of the proposed approach.