Criteria based on mutual information minimization for blind source separation in post nonlinear mixtures

Extracting independent source signals from their nonlinear mixtures is a very important issue in many realistic models. This paper proposes a new method for solving nonlinear blind source separation (NBSS) problems by exploiting particle swarm optimization (PSO) algorithm and natural gradient descent. First, we address the problem of separation of mutually independent sources in post-nonlinear mixtures. The natural gradient descent is used to estimate the separation matrix. Then we define the mutual information between output signals as the fitness function of PSO. The mutual information is used to measure the statistical dependence of the outputs of the demixing system. PSO can rapidly obtain the globally optimal coefficients of the higher order polynomial functions. Compared to conventional NBSS approaches, the main characteristics of this method are its simplicity, the rapid convergence and high accuracy. In particular, it is robust against local minima in search for inverse functions. Experiments are discussed to demonstrate these results.

The problem of blind source separation (BSS) has been intensively studied by the signal processing community. The first solutions to deal with BSS were proposed in the 1980's and are founded on the concept of independent component analysis (ICA). More recently, aiming at tackling some limitations of ICA-based methods, much attention has been paid to alternative BSS approaches. In this tutorial, in addition to providing a brief review of the classical BSS framework, we present two research trends in this area, namely source separation over Galois fields and sparse component analysis. For both subjects, we provide an overview of the main criteria, highlighting scenarios that can benefit from these more recent BSS paradigms.

A new method for solving the permutation problem in the frequency-domain Blind Source Separation(BSS) was presented.This new method divided the whole frequency-domain into three sections and applied different permutation algorithms to different sections.The neighboring frequency correlation and harmonic frequency correlation coefficient of signal amplitudes were used together for the low-frequency section,the direction of arrival estimation for speech sources for the mid-frequency section,and the combination of correlation coefficient comparison and direction estimation for the high-frequency section,respectively.Experimental results show that the new method provides a more robust and precise solution to the permutation problem than the algorithm only with interfrequency correlation coefficient of signal amplitudes or only with direction of arrival estimation for sources.

We address the problem of blind source separation of non-stationary signals of which only instantaneous linear mixtures are observed. A blind source separation approach exploiting both auto-terms and cross-terms of the time-frequency (TF) distributions of the sources is considered. The approach is based on the simultaneous diagonalization and anti-diagonalization of spatial TF distribution matrices made up of, respectively, auto-terms and cross-terms. Numerical simulations are provided to demonstrate the effectiveness of the proposed approach and compare its performances with existing TF-based methods.

An improvement in the multimodal approach to the problem of blind source separation (BSS) of moving sources is proposed. The challenge of BSS for moving sources is that the mixing filters are time varying. Thus the unmixing filters should also be time varying, which are difficult to calculate from only statistical information avail able from limited number of audio samples. Therefore, in the pro posed approach a robust least square frequency invariant data independent (RLSFIDI) beamformer is implemented to perform real time speech enhancement and provide separation of the moving sources. Direction of arrival information of the sources is obtained from the visual 3-D tracker based on a Markov Chain Monte Carlo particle filter (MCMC-PF). The uncertainties in source localization and direction of arrival information are controlled by using convex optimization approach in the beamformer design. This provides robust ness with a wider main lobe for source of interest (SOI) and wider attenuation pattern to block the interference. In addition, white noise gain (WNG) constraint is used to control the beamformer sensitivity. Experimental results show that by utilizing RLSFIDI beamformer a significant improvement in BSS performance for moving sources is achieved in a low reverberant environment.

The problem of blind source separation (BSS) for multiple-input multiple-output (MIMO) autoregressive (AR) mixtures is addressed in this paper. A new time-domain method for system identification and BSS is proposed based on the Gaussian mixture model (GMM) for sources distribution. The algorithm is based on the generalized expectation-maximization (GEM) method for joint estimation of the AR model parameters and the GMM parameters of the sources. The method is tested via simulations of synthetic and real audio signals. The results show that the proposed algorithm outperforms the well-known multidimensional linear predictive coding (LPC), and it achieves higher signal-to-interference ratio (SIR) in the BSS problem.

In this paper, we address the problem of underdetermined blind source separation (BSS) of anechoic speech mixtures. We propose a demixing algorithm that exploits the sparsity of certain time-frequency expansions of speech signals. Our algorithm merges lscrq -basis-pursuit with ideas based on the degenerate unmixing estimation technique (DUET) [Yiotalmaz and Rickard, Blind Source Separation of Speech Mixtures via Time-Frequency Masking, IEEE Transactions on Signal Processing, vol. 52, no. 7, pp. 1830-1847, July 2004]. There are two main novel components to our approach: 1, our algorithm makes use of all available mixtures in the anechoic scenario where both attenuations and arrival delays between sensors are considered, without imposing any structure on the microphone positions, and 2, we illustrate experimentally that the separation performance is improved when one uses lscrq-basis-pursuit with q < 1 compared to the q = 1 case. Moreover, we provide a probabilistic interpretation of the proposed algorithm that explains why a choice of 0.1 les q les 0.4 is appropriate in the case of speech. Experimental results on both simulated and real data demonstrate significant gains in separation performance when compared to other state-of-the-art BSS algorithms reported in the literature.

We consider the problem of blind source separation of independent signals which passed through a multi-input multi-output linear time-invariant system. An approximate maximum likelihood estimator and its performance were studied by Yellin and Friedlander (see IEEE Trans. Signal Processing, vol.47, no.5, p.1410-14, 1999, and vol.47, no.6, p.1542-58). The results derived therein are used here to study the performance of source separation techniques based on high order statistics.

In the case of multiple nonstationary independent source signals and linear instantaneous time-varying mixing systems, it is difficult to adaptively separate the multiple source signals. Therefore, the adaptive blind source separation (BSS) problem is firstly formally expressed and compared with tradition BSS problem. Then, we propose an adaptive blind identification and separation method based on the variable learning rate equivariant adaptive source separation via independence (EASI) algorithm. Furthermore, we analyze the scope and conditions of variable-learning rate EASI algorithm. The adaptive BSS simulation results also show that the variable learning rate EASI algorithm provides better separation effect than the fixed learning rate EASI and recursive least-squares algorithms.

We present a new speaker-separation algorithm for separating signals with known statistical characteristics from mixed multi-channel recordings. Speaker separation has conventionally been treated as a problem of blind source separation (BSS). This approach does not utilize any knowledge of the statistical characteristics of the signals to be separated, relying mainly on the independence between the various signals to separate them. We present an algorithm that utilizes detailed statistical information about the signals to be separated, represented in the form of hidden Markov models (HMM). We treat the signal separation problem as one of beamforming, where each signal is extracted using a filter-and-sum array. The filters are estimated to maximize the likelihood of the summed output, measured on the HMM for the desired signal. This is done by iteratively estimating the best state sequence through the HMM from a factorial HMM (FHMM) that is the cross-product of the HMMs for the multiple signals, using the current output of the array, and estimating the filters to maximize the likelihood of that state sequence. Experiments show that the proposed method can cleanly extract a background speaker who is 20 dB below the foreground speaker in a two-speaker mixture, when the HMMs for the signals are constructed from knowledge of the utterance transcriptions.

This paper deals with the problem of blind source separation which consists of recovering a set of signals from instantaneous linear mixture of them. So far, this problem has been solved using statistical information available on the source signals. Here, we propose an approach for blind source separation based on time-frequency (t-f) signal representations. This approach is based on a `joint diagonalization' of a combined set of time frequency distribution matrices which correspond to different t-f points. It relies on the difference in the t-f signatures of the sources to be separated. In contrast to existing techniques, the proposed approach allows the separation of Gaussian sources with identical spectra shape. Because of changes incurred in the t-f signal structures due to time- delay, the new approach can be employed to separate multipath signals received by multi-sensor array. Moreover, the effects of spreading the noise power while localizing the source energy in the time frequency domain amounts to increasing the signal to noise ratio and hence improved performance. Numerical examples are provided to illustrate the effectiveness of our method.

This paper studies the problem of blind source separation (BSS) under the assumption that the source signals are cyclostationary. Attention is restricted to methods based on second-order cyclostationary statistics (SOCS). Necessary and sufficient conditions for SOCS-based identifiability and SOCS-based separability are presented. Algorithms are developed to achieve BSS using only SOCS.

This paper describes a method for solving the permutation problem of frequency-domain blind source separation (BSS). The method analyzes the mixing system information estimated with independent component analysis (ICA). When we use widely spaced sensors or increase the sampling rate, spatial aliasing may occur for high frequencies due to the possibility of multiple cycles in the sensor spacing. In such cases, the estimated information would imply multiple possibilities for a source location. This causes some difficulty when analyzing the information. We propose a new method designed to overcome this difficulty. This method first estimates the model parameters for the mixing system at low frequencies where spatial aliasing does not occur, and then refines the estimations by using data at all frequencies. This refinement leads to precise parameter estimation and therefore precise permutation alignment. Experimental results show the effectiveness of the new method.

This paper deals with the problem of blind source separation in fMRI data analysis. Our main contribution is to present a maximum likelihood based method to blindly separate the brain activations in an fMRI experiment. Choosing the time frequency domain as the signal representation space, our method relies on the second order statistics and exploits the inter-source diversity. It is efficiently implemented by the EM (expectation-maximization) algorithm where the time courses of the brain activations are considered as the hidden variables. The estimation variance of the STFT (short time Fourier transform) is reduced by averaging across time frequency sub-domains. The successful separation of the right and left visual cortex activations during a visual fMRI experiment, in a block design, and the extraction of only the relevant tasks corroborate the effectiveness of our proposed separating algorithm.

We address the problem of Blind Source Separation (BSS) of superimposed signals in situations where one signal has constant or slowly varying intensities at some consecutive locations and at the corresponding locations the other signal has highly varying intensities. Independent Component Analysis (ICA) is a major technique for Blind Source Separation and the existing ICA algorithms fail to estimate the original intensities in the stated situation. We combine the advantages of existing sparse methods and Kernel ICA in our technique, by proposing wavelet packet based sparse decomposition of signals prior to the application of Kernel ICA. Simulations and experimental results illustrate the effectiveness and accuracy of the proposed approach. The approach is general in the way that it can be tailored and applied to a wide range of BSS problems concerning one-dimensional signals and images (two-dimensional signals).