Independent component analysis based on first-order statistics

Abstract

This communication puts forward a novel method for independent source extraction in instantaneous linear mixtures. The method is based on the conditional mean of the whitened observations and requires some prior knowledge of the positive support of the desired source. A theoretical performance analysis yields the closed-form expression of the asymptotic interference-to-signal ratio (ISR) achieved by this technique. The analysis includes the effects of inaccuracies in the estimation of the positive support of the desired source in single-step and iterative implementations of the algorithm. Numerical experiments validate the fitness of the asymptotic approximations. As it is based on first-order statistics, the method is extremely cost-effective, which makes it an attractive alternative to second-and higher-order statistical techniques in power-limited scenarios.

Fast Extraction for Skewed Source Signals Using Conditional Expectation

“…Since the first-order statistics-based algorithms [6][7][8] generally extract the source of interest under the condition that the mixing matrix is a unitary matrix, they can be only used in the determined case. In this paper, we remove this condition and obtain the column vector of the mixing matrix corresponding to the desired source based on the conditional expectation shown by…”

“…The existing extraction algorithms mainly employ the second-and higher-order statistics by exploiting the statistical independence of the sources, and some of them need to preprocess the mixture data such as FastICA [5]. Recently, Zarzoso et al [6] and Xu et al [7] and Xu and Shen [8] proposed a class of more computationally efficient algorithms for independent source extraction based on the first-order statistics as well as the conditional expectation. But before performing this class of algorithm, it requires to know the time indices where the source of interest is positive, that is, the positive support of the desired source, which reduces the practicability of this class of algorithm.…”

“…It does not require the prior knowledge of the positive support of the desired source and can be applied both in the determined and underdetermined cases. It should be noted that after obtaining the source signal with the maximal absolute value of skewness, the source signal with the second maximal absolute value of skewness can also be extracted by the proposed algorithm from the mixtures which subtract the component of the estimated source (e.g., through linear regression as in [6]). Likewise, if required, the other skewed source signals with different skewness can be gained sequentially.…”

Convolutive Independent Component Analysis Based on First-order Statistics for Complex-valued Source Extraction

“…To quantify source extraction performance, we refer to [15] and define the average ISR per interfering source as…”

“… If the prior knowledge of positive support is accurate enough (r>0.9), using single-step separators given in (11), (15) and (16) is a satisfactory choice to achieve extraction efficiently. But iterative separators should be preferable to improve the performance when the accuracy of prior knowledge is poor (0.5<r<0.9).…”