Fast fixed-point independent vector analysis algorithms for convolutive blind source separation

Independent vector analysis (IVA) is a special form of independent component analysis (ICA), which has demonstrated its prominent performance in solving convolutive blind source separation (BSS) problems in the frequency domain. Most IVA algorithms are based on optimizing certain contrast functions, where the main difficulty of these approaches lies in finding a reliable and fast estimation of the unknown distribution of sources. Despite the rich availability of efficient tensorial approaches to the standard ICA problem, these methods have not been explored considerably for IVA. In this article, we propose a matrix joint diagonalization approach to solve the complex IVA problem. The new factorization neither relies on a whitening process, nor does it require an estimate of the joint probability distribution of the dependent signal groups. The latter is in contrast to most IVA approaches up to date. The underlying geometry of the problem is investigated together with a critical point analysis of the resulting cost function. A conjugate gradient algorithm on the appropriate manifold setting is developed.

We propose a new algorithm for blind source separation (BSS), in which independent component analysis (ICA) and beamforming are combined to resolve the low-convergence problem through optimization in ICA. The proposed method consists of the following three parts: (1) frequency-domain ICA with direction-of-arrival (DOA) estimation; (2) null beamforming based on the estimated DOA; (3) integration of (1) and (2) based on the algorithm diversity in both iteration and frequency domain. The inverse of the mixing matrix obtained by ICA is temporally substituted by the matrix based on null beamforming through iterative optimization, and the temporal alternation between ICA and beamforming can realize fast- and high-convergence optimization. The results of the signal separation experiments reveal that the signal separation performance of the proposed algorithm is superior to that of the conventional ICA-based BSS method, even under reverberant conditions.

A new independent component analysis (ICA) formulation called independent vector analysis (IVA) was proposed in order to solve the permutation problem in convolutive blind source separation (BSS). Instead of running ICA in each frequency bin separately and correcting the disorder with an additional algorithmic scheme afterwards, IVA exploited the dependency among the frequency components of a source and dealt with them as a multivariate source by modeling it with sparse and spherically, or radially, symmetric joint probability density functions (pdfs). In this paper, we compare the speech separation performances of IVA by using a group of l <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sup> -norm-invariant sparse pdfs where the value of and the sparseness can be controlled. Also, we derive an IVA algorithm from a nonparametric perspective with the constraint of spherical symmetry and high dimensionality. Simulation results confirm the efficiency of assuming sparseness and spherical symmetry for the speech model in the frequency domain.

Blind single-channel source separation is a long-standing machine learning and signal processing problem. Traditional blind source separation (BSS) algorithms were proposed to solve this task utilizing multiple signal constraints. Generative adversarial network (GAN) are free from statistical constraints and samples, but the role of adversarial training in the task of BSS has not been fully demonstrated. Therefore, a new separation network model that enables to learn the known separated signal distribution from the stepwise fine estimation of the unknown mixture distribution was presented in this paper, and a self-attention mechanism was introduced to solve the problem of the blurring details of the generated image by the generator which preserves image details in the process of image separation. Compared with the existing single-channel blind source separation algorithm based on generative adversarial network-neural egg separation (NES), the detailed information of this new separation algorithm is more prominent, and the source signal in the mixed image has been separated more effectively, and has better separation performance than the classic blind source separation algorithms.

We propose a new algorithm for blind source separation (BSS), in which independent component analysis (ICA) and beamforming are combined to resolve the low-convergence problem through optimization in ICA. The proposed method consists of the following three parts: (1) frequency-domain ICA with direction-of-arrival (DOA) estimation, (2) null beamforming based on the estimated DOA, and (3) integration of (1) and (2) based on the algorithm diversity in both iteration and frequency domain. The inverse of the mixing matrix obtained by ICA is temporally substituted by the matrix based on null beamforming through iterative optimization, and the temporal alternation between ICA and beamforming can realize fast- and high-convergence optimization. The results of the signal separation experiments reveal that the signal separation performance of the proposed algorithm is superior to that of the conventional ICA-based BSS method, even under reverberant conditions.

Independent vector analysis followed by HMM-based feature enhancement for robust speech recognition

Electrocardiogram (ECG) signals are normally contaminated by various physiological and nonphysiological artifacts. Among these artifacts baseline wandering, electrode movement and muscle artifacts are particularly difficult to remove. Independent component analysis (ICA) is a well-known technique of blind source separation (BSS) and is extensively used in literature for ECG artifact elimination. In this article, the independent vector analysis (IVA) is used for artifact removal in the ECG data. This technique takes advantage of both the canonical correlation analysis (CCA) and the ICA due to the utilization of second-order and high order statistics for un-mixing of the recorded mixed data. The utilization of recorded signals along with their delayed versions makes the IVA-based technique more practical. The proposed technique is evaluated on real and simulated ECG signals and it shows that the proposed technique outperforms the CCA and ICA because it removes the artifacts while altering the ECG signals minimally.

The aim of this paper is to solve the blind source separation (BSS) problem using the temporal independent component analysis (ICA) model. In contrast to ordinary ICA, except for independent assumption, the temporal structure of the source components is taken into account. After combing the virtues of both high order statistics and the temporal second-order information of the source signals, we can get the novel strengthened BSS algorithm-STICA algorithm by using the joint approximate diagonalisation of eigen-matrices (JADE) method. The proposed STICA can not only separate the spatial independent random variables but also the spatial independent time series or both of them exist simultaneously, especially when the sources have non-symmetric distributed time series.

In the recent past, blind source separation (BSS) algorithms using multivariate statistical data analysis technique have been successfully used for source identification and separation in the field of biomedical and statistical signal processing. Recently numbers of different BSS techniques have been developed. With BSS methods being the feasible method for source separation and decomposition of biosignals, it is important to compare the different techniques and determine the most suitable method for the applications. This paper presents the performance of five BSS algorithms (SOBI, TDSEP, FastICA, JADE and Infomax) for decomposition of sEMG to identify subtle finger movements. It is observed that BSS algorithms based on second-order statistics (SOBI and TDSEP) gives better performance compared to algorithms based on higher-order statistics (FastICA, JADE and infomax).

A new blind image source separation algorithm based on feedback sparse component analysis

To solve the problem of joint blind equalization and source separation, two new quasi-Newton 'adaptive algorithms with rapid convergence property are proposed based upon the cross-correlation and constant modulus (CC-CM) criterion, namely the block-Shanno cross-correlation and constant modulus algorithm (BS-CCCMA) and the fast quasi-Newton cross-correlation and constant modulus algorithm (FQN-CCCMA). Simulations studies are used to show that the convergence properties of these algorithms are much improved upon those of the conventional LMS-CCCMA algorithm.

Most algorithms for blind source separation (BSS) or independent component analysis (ICA) assume an equal number of sources as sensors. For multichannel electrophysiological recordings, such as the electroencephalogram (EEG), however, there are often far fewer sources of neurophysiologically relevant activity than the number of sensors. This adds a model order estimation problem to the source separation problem. Conventional estimates of the number of sources are based on the dominant eigenvalues of the data covariance matrix, obtained from principal component analysis (PCA), whose corresponding eigenvectors are also used for prewhitening. It is well known that PCA is susceptible to noise, leading to incorrect model order estimates and data distortion, which in turn limit the accuracy of the source estimates. It is therefore highly desirable to determine the correct number of sources and their spatial topographies directly, without PCA-based data truncation or prewhitening. In this work, we present a stepwise BSS method for extracting only the sources necessary for a sufficiently good least-square fit to the data. This simultaneously yields model order and source estimates, which we examine at different noise levels. We also show how only a few neurophysiologically meaningful components can be extracted from 25-channel ictal EEG.

In this paper, we present a quasi-Newton (QN) algorithm for joint independent subspace analysis (JISA). JISA is a recently proposed generalization of independent vector analysis (IVA). JISA extends classical blind source separation (BSS) to jointly resolve several BSS problems by exploiting statistical dependence between latent sources across mixtures, as well as relaxing the assumption of statistical independence within each mixture. Algebraically, JISA based on second-order statistics amounts to coupled block diagonalization of a set of covariance and cross-covariance matrices, as well as block diagonalization of a single permuted covariance matrix. The proposed QN algorithm achieves asymptotically the minimal mean square error (MMSE) in the separation of multidimensional Gaussian components. Numerical experiments demonstrate convergence and source separation properties of the proposed algorithm.KeywordsBlind source separationIndependent vector analysisIndependent subspace analysisJoint block diagonalization

This paper proposes a Constrained Least Square approach to the problem of Blind Source Separation (BSS) in a non-stationary mixing environment. Initially the demixing matrix is identified for the nominal system using the standard Kullback-Liebler(KL) divergence minimization technique. The KL algorithm is computationally expensive requiring longer CPU time and a large collection of samples. Therefore for small or structured changes in the mixing system which may occur due to environmental conditions this algorithm may be slow and inappropriate in certain applications. In this paper we have proposed an algorithm based on Constrained Least Square that utilizes the initially estimated demixing structure from the KL algorithm to find the new structure for the changed system. It is computationally faster even for larger number of samples. The assumptions are that the changes are infrequent and the statistical properties of the sources do not change. The performance of the technique has been compared with existing methods.

Blind Source Separation (BSS) algorithms based on the noise-free model are not applicable when the Signal Noise Ratio (SNR) is low. In view of this situation, our solution is to denoise the mixtures with additive white Gaussian noise firstly, and then use BSS algorithms. This paper proposes a piecewise Empirical Mode Decomposition (EMD) thresholding approach to denoise mixtures with strong noise. This approach can distinguish the noise-dominated IMFs and signal-dominated IMFs, and then respectively apply different thresholdings methods. Simulation results show that compared with the Wavelet denoising, the proposed approach has a better denoising performance, and can remarkably enhance the separation performance of BSS algorithms, especially when the signal SNR is low.