Blind Deconvolution of Sources in Fourier Space Based on Generalized Laplace Distribution

Blind Deconvolution of Sources in Fourier Space Based on Generalized Laplace Distribution

M. El-Sayed Waheed (Department of Computer Science, Suez Canal University, Ismailia, Egypt), Mohamed-H Mousa (Department of Computer Science, Suez Canal University, Ismailia, Egypt) and Mohamed-K Hussein (Department of Computer Science, Suez Canal University, Ismailia, Egypt)
Copyright: © 2013 |Pages: 11
DOI: 10.4018/ijsda.2013040104
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Abstract

An approach to multi-channel blind de-convolution is developed, which uses an adaptive filter that performs blind source separation in the Fourier space. The approach keeps (during the learning process) the same permutation and provides appropriate scaling of components for all frequency bins in the frequency space. Experiments indicate that Generalized Laplace Distribution can be used effectively to blind de-convolution of convolution mixtures of sources in Fourier space compared to the conventional Laplacian and Gaussian function.
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2. The Bss/Mbd Problems

The blind source separation task. Assume that there exist zero-mean source signals, , that are scalar valued and mutually (spatially) statistically independent (or as independent as possible) at each time instant or index value number of sources (Amari, Douglas, Cichocki, & Yang, 1997; Cichocki & Amari, 2002). Denote the m-dimensional -th mixture data vector, at discrete index value (time) t. The blind source separation (BSS) mixing model is equal to:

(1) where N is noise signal. A well-known iterative optimization method is the stochastic gradient (or gradient descent) search (Zeckhauser & Thompson, 1970). In this method the basic task is to define a criterion , which obtains its minimum for some if this is the expected optimum solution. Applying the natural gradient descent approach (Amari, Douglas, Cichocki, & Yang, 1997; Cichocki & Amari, 2002) with the cost function, based on Kullback-Leibler divergence, we may derive the learning rule for BSS:

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