Energy predictability to blind source separation

Blind Source Separation Using Quadratic form Innovation

“…which is the EP contrast function for BSS presented in the paper [22] when the autoregressive model has just one predicting term.…”

“…In the EP method [22] or the nonlinear innovation method [24], the authors present the following constrained minimization problem based on the generalized autocorrelation error function of the desired source using just one predicting term:…”

“…In this experiment, we consider the separation of the following ten source signals with 5,000 time points: five signals with linear autocorrelations (s i (t) = sin(i2π30t/5, 000), for i = 1, 2, 3, 4, 5) and five signals with square autocorrelations (s i (t), i = 6, 7, 8, 9, 10) 1 (taken from [22], with Gaussian marginal distributions, zero linear autocorrelations and square temporal autocorrelations). The waveforms of ten original signals are shown in Fig.…”

“…(a) The FastICA [13] based on non-Gaussianity; (b) The JADE [5] using the high-order cumulants; (c) Second Order Blind Identification (SOBI) [4] by joint diagonalization of linear correlation matrices, based on second order statistics and linear predictability; (d) CP [11], which combines the non-Gaussianity and the linear predictability for BSS; (e) EP [22] to BSS; (f) Nonlinear innovation (MINDIFF) [24] to BSS; (g) The cumulant-based fixed-point approach using the nonstationarity of variance (FPNSV) [12]; (h) The proposed QFBSS algorithm using quadratic form innovation (G(u) = log(cosh(u)); the learning rates µ w i = 1, µ r i = 0.01, µ α i = 0.01 and τ = 1).…”

“…The BSS problem has been studied by researchers in applied mathematics, neural networks and statistical signal processing. Several methods for BSS using the statistical properties of original sources have been proposed, such as non-Gaussianity (or equivalently, independent component analysis, ICA) [1,3,[5][6][7][8][9][10][13][14][15], or time-structure information, such as linear predictability or smoothness [2,7,16,17], linear autocorrelation [4,19,27], coding complexity [11,21,23,25], temporal predictability [26], nonstationarity [12,18,20], energy predictability (EP) [22], or nonlinear innovation [24], etc.…”