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Abstract: Blind source extraction (BSE) is a special class of blind source separation (BSS) method. Due to its low computation load and fast processing speed, BSE has become one of the promising methods in signal processing and analysis. This paper addresses BSE problem when a desired source signal has temporal structures. Based on the generalized autocorrelations of the desired signal and the non-Gaussianity of its innovations, we develop an objective function. Maximizing this objective function, we present a BSE algorithm and further give its stability analysis in this paper. Simulations on image data and electrocardiogram (ECG) data indicate its better performance and the better property of tolerance to the estimation error of the time delay. [Copyright &y& Elsevier]

Abstract: This paper addresses blind source separation (BSS) problem when source signals have the temporal structure with nonlinear autocorrelation. Using the temporal characteristics of sources, we develop an objective function based on the nonlinear autocorrelation of sources. Maximizing the objective function, we propose a fixed-point source separation algorithm. Furthermore, we give some mathematical properties of the algorithm. Computer simulations for sources with square temporal autocorrelation and the real-world applications in the analysis of the magnetoencephalographic recordings (MEG) illustrate the efficiency of the proposed approach. Thus, the presented BSS algorithm, which is based on the nonlinear measure of temporal autocorrelation, provides a novel statistical property to perform BSS. [Copyright &y& Elsevier]

Abstract: A unifying model that combines three properties is proposed by Hyvärinen, and a gradient ascent algorithm for independent component analysis (ICA) is performed by maximum likelihood estimation. In this paper, we consider the estimation of the data model of ICA when Gaussian noise is present and the independent components are time dependent. Firstly, according to the useful property of Gaussian moments, we introduce Gaussian moments algorithm to estimation of the noisy unifying model when the noise covariance matrix is known. Next, when the noise covariance is unknown, a new Gaussian moments algorithm is developed. Finally, the validity and performance of our algorithms are demonstrated by computer simulations. [Copyright &y& Elsevier]

Abstract: This paper addresses the problem of blind source separation and presents a fixed-point nonlinear principal component analysis (NPCA) algorithm. It is a block-wise batch algorithm and gives an alternative perspective on existing adaptive online NPCA algorithms. Utilizing new activation functions that automatically satisfy a stability condition, the proposed algorithm can separate mixed signals with sub- and super-Gaussian source distributions. The efficiency is confirmed by extensive computer simulations on man-made sources as well as practical speech signals. [Copyright &y& Elsevier]

Blind source separation represents a signal processing technique with a large potential for noise reduction. However, its application in modern digital hearing aids poses high demands with respect to computational efficiency and speed of adaptation towards the desired solution. In this paper, an algorithm is presented which fulfills these goals under the idealized assumption that the superposition of sources in rooms can be approximated as a superposition under anechoic conditions. Specifically, attenuation, the signals’ finite propagation speed, and diffuse noise are accounted for, whereas reflections and reverberation are considered as negligible effects. This approximation is referred to as the ‘free field’ assumption. Starting from a general blind source separation algorithm for Fourier transformed speech signals, the free field assumption is incorporated into the framework, yielding a simple, fast and adaptive algorithm that is able to track moving sources. Implementation details are given which were found to be indispensable for fast and robust signal separation. Performance is evaluated both by simulations and experimentally, including separation of a moving and a fixed speaker in a recorded real anechoic environment. The potential benefits and shortcomings of this algorithm are discussed with regard to its inclusion into the signal processing framework of digital hearing aids for real reverberant acoustic situations. [Copyright &y& Elsevier]