A convex geometry-based blind source separation method for separating nonnegative sources

This paper presents a convex geometry (CG)-based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be column-sum-to-one by mapping the available observation matrix. Then, its zero-samples are found by searching the facets of the convex hull spanned by the mapped observations. Considering these zero-samples, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CG-based method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method.

Quantitative evaluation of artifact removal in real magnetoencephalogram signals with blind source separation

The magnetoencephalogram (MEG) is contaminated with undesired signals, which are called artifacts. Some of the most important ones are the cardiac and the ocular artifacts (CA and OA, respectively), and the power line noise (PLN). Blind source separation (BSS) has been used to reduce the influence of the artifacts in the data. There is a plethora of BSS-based artifact removal approaches, but few comparative analyses. In this study, MEG background activity from 26 subjects was processed with five widespread BSS (AMUSE, SOBI, JADE, extended Infomax, and FastICA) and one constrained BSS (cBSS) techniques. Then, the ability of several combinations of BSS algorithm, epoch length, and artifact detection metric to automatically reduce the CA, OA, and PLN were quantified with objective criteria. The results pinpointed to cBSS as a very suitable approach to remove the CA. Additionally, a combination of AMUSE or SOBI and artifact detection metrics based on entropy or power criteria decreased the OA. Finally, the PLN was reduced by means of a spectral metric. These findings confirm the utility of BSS to help in the artifact removal for MEG background activity.

On the Quotient Function Employed in the Blind Source Separation Problem

MSC 2010: 42C40, 94A12

Blind source separation dependent component analysis

This book provides readers a complete and self-contained set of knowledge about dependent source separation, including the latest development in this field. The book gives an overview on blind source separation where three promising blind separation techniques that can tackle mutually correlated sources are presented. The book further focuses on the non-negativity based methods, the time-frequency analysis based methods, and the pre-coding based methods, respectively.

Microphone array beamforming approach to blind speech separation

In this paper, we present a microphone array beamforming approach to blind speech separation. Unlike previous beamforming approaches, our system does not require a-priori knowledge of the microphone placement and speaker location, making the system directly comparable other blind source separation methods which require no prior knowledge of recording conditions. Microphone location is automatically estimated using an assumed noise field model, and speaker locations are estimated using cross correlation based methods. The system is evaluated on the data provided for the PASCAL Speech Separation Challenge 2 (SSC2), achieving a word error rate of 58% on the evaluation set.

A new blind signal separation algorithm for instantaneous MIMO system

We address the problem of adaptive blind source separation (BSS) from instantaneous multi-input multi-output (MIMO) channels. In this paper, we propose a new constant modulus (CM)-based algorithm which employ nonlinear function as the de-correlation term. Moreover, it is shown by theoretical analysis that the proposed algorithm has less mean square error (MSE), i.e., better separation performance, in steady state than the cross-correlation and constant modulus algorithm (CC-CMA). Numerical simulations show the effectiveness of the proposed result.

New blind source estimation methods based on constant modulus criterion

This thesis presents two novel algorithms for blind chancel equalization (BCE) and blind source separation (BSS). Beside these, a general framework for global convergent analysis is proposed. Finally, the open problem of equalising a non-irreducible system is answered by the algorithm proposed in this thesis.

Functional source separation applied to induced visual gamma activity

Objective of this work was to explore the performance of a recently introduced source extraction method, FSS (Functional Source Separation), in recovering induced oscillatory change responses from extra-cephalic magnetoencephalographic (MEG) signals. Unlike algorithms used to solve the inverse problem, FSS does not make any assumption about the underlying biophysical source model; instead, it makes use of task-related features (functional constraints) to estimate source/s of interest. FSS was compared with blind source separation (BSS) approaches such as Principal and Independent Component Analysis, PCA and ICA, which are not subject to any explicit forward solution or functional constraint, but require source uncorrelatedness (PCA), or independence (ICA). A visual MEG experiment with signals recorded from six subjects viewing a set of static horizontal black/white square-wave grating patterns at different spatial frequencies was analyzed. The beamforming technique Synthetic Aperture Magnetometry (SAM) was applied to localize task-related sources; obtained spatial filters were used to automatically select BSS and FSS components in the spatial area of interest. Source spectral properties were investigated by using Morlet-wavelet time-frequency representations and significant task-induced changes were evaluated by means of a resampling technique; the resulting spectral behaviours in the gamma frequency band of interest (20-70 Hz), as well as the spatial frequency-dependent gamma reactivity, were quantified and compared among methods. Among the tested approaches, only FSS was able to estimate the expected sustained gamma activity enhancement in primary visual cortex, throughout the whole duration of the stimulus presentation for all subjects, and to obtain sources comparable to invasively recorded data.

A new algorithm for blind separation of cyclostationary source from linear mixtures

This paper addresses the problem of separating a cyclostationary source from linear mixtures. It first shows that if the cyclic frequencies of the source of interest are known and different from those of the interfering sources, perfect source separation can be achieved using the proposed separation criterion. Then an algorithm is derived to perform the blind source separation. Simulation results demonstrate the validity of the proposed algorithm

Blind separation of cyclostationary sources based on phase-frequency redundancy

Thin paper presents a new algorithm for blind source separation (BSS) by exploiting phase and frequency redundancy of cyclostationary signals in a complementary way. The separation criterion is to diagonalize a polynomial matrix whose coefficient matrices consist of the correlation and cyclic correlation matrices of multiple measurements. Computer simulation results illustrate, the performance of the new algorithm in comparison with some existing algorithms.

Blind separation of cyclostationary signals from instantaneous mixtures

This paper presents a new approach for blind separation of unknown cyclostationary signals from instantaneous mixtures. The proposed method can perfectly separate the mixed source signals so long as they have either different cyclic frequencies or clock phases. This is a weaker condition than those required by the algorithms. The separation criterion is to diagonalize a polynomial matrix whose coefficient matrices consist of the correlation and cyclic correlation matrices, at time delay τ=0, of multiple measurements.