By Cichocki A., Amari Sh.-H.

With stable theoretical foundations and various strength functions, Blind sign Processing (BSP) is without doubt one of the most well-liked rising parts in sign Processing. This quantity unifies and extends the theories of adaptive blind sign and snapshot processing and gives useful and effective algorithms for blind resource separation, self reliant, primary, Minor part research, and Multichannel Blind Deconvolution (MBD) and Equalization. Containing over 1400 references and mathematical expressions Adaptive Blind sign and snapshot Processing supplies an remarkable selection of necessary suggestions for adaptive blind signal/image separation, extraction, decomposition and filtering of multi-variable indications and knowledge.

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14 INTRODUCTION TO BLIND SIGNAL PROCESSING: PROBLEMS AND APPLICATIONS Reference noise nR(k) Unknown H1(z) s1(k) + h11 x1(k) w1n h1n H (z ) h21 2 + h22 w21 x2(k) sn(k) Fig. 8 hnn h n1 w22 W2(z) _ y2(k) w2n h2 n hn 2 y1(k) w12 h12 s2(k) w11 W1(z) _ wn1 Hn(z) + wn2 xn(k) wnn Wn(z) _ yn(k) Illustration of noise cancellation and blind separation - deconvolution problem. In a traditional linear Finite Impulse Response (FIR) adaptive noise cancellation filter, the noise is estimated as a weighted sum of delayed samples of the reference interference.

3 : (a) Basic FIR filter model, (b) Gamma filter model, (c) Laguerre filter model. where P is an n × n permutation matrix, D(z) is an n × n diagonal matrix whose (i, i)-th entry is ci z −∆i , ci is a non-zero scalar factor, and ∆i is an integer delay. We assume that both H(z) and W(z, k) are stable with non-zero eigenvalues on the unit circle |z| = 1. In addition, the derivatives of quantities with respect to W(z, k) can be understood as a series of matrices indexed by the lag p of Wp (k) [38, 39, 612].

Of sources (mainly second-order correlations) and/or the nonstationarity of sources, lead to the second-order BSS methods. In contrast to BSS methods based on HOS, all the secondorder statistics based methods do not have to infer the probability distributions of sources or nonlinear activation functions. 3 Independent Component Analysis for Noisy Data As the estimation of a separating (unmixing) matrix W and a mixing matrix H in the presence of noise is rather difficult; the majority of past research efforts have been devoted to only the noiseless case, where ν(k) = 0.