Source Separation Of Signals Research Articles

A Mathematical Model for Source Separation of MMG Signals Recorded With a Coupled Microphone-Accelerometer Sensor Pair

Recent advances in sensor technology for muscle activity monitoring have resulted in the development of a coupled microphone-accelerometer sensor pair for physiological acousti signal recording. This sensor can be used to eliminate interfering sources in practical settings where the contamination of an acoustic signal by ambient noise confounds detection but cannot be easily removed [e.g., mechanomyography (MMG), swallowing sounds, respiration, and heart sounds]. This paper presents a mathematical model for the coupled microphone-accelerometer vibration sensor pair, specifically applied to muscle activity monitoring (i.e., MMG) and noise discrimination in externally powered prostheses for below-elbow amputees. While the model provides a simple and reliable source separation technique for MMG signals, it can also be easily adapted to other aplications where the recording of low-frequency (< 1 kHz) physiological vibration signals is required.

Blind deconvolution of images using optimal sparse representations

The relative Newton algorithm, previously proposed for quasi-maximum likelihood blind source separation and blind deconvolution of one-dimensional signals is generalized for blind deconvolution of images. Smooth approximation of the absolute value is used as the nonlinear term for sparse sources. In addition, we propose a method of sparsification, which allows blind deconvolution of arbitrary sources, and show how to find optimal sparsifying transformations by supervised learning.

Blind source separation of acoustic signals in realistic environments based on ICA in the time‐frequency domain

We present an approach for blind separation of acoustic sources produced from multiple speakers mixed in realistic room environments. We first transform recorded signals into the time‐frequency domain to make mixing become instantaneous. We then separate the sources in each frequency bin based on an independent component analysis (ICA) algorithm. For the present paper, we choose the complex version of fixedpoint iteration (CFPI), i.e. the complex version of FastICA, as the algorithm. From the separated signals in the time‐frequency domain, we reconstruct output‐separated signals in the time domain. To solve the so‐called permutation problem due to the indeterminacy of permutation in the standard ICA, we propose a method that applies a special property of the CFPI cost function. Generally, the cost function has several optimal points that correspond to the different permutations of the outputs. These optimal points are isolated by some non‐optimal regions of the cost function. In different but neighboring bins, optimal points with the same permutation are at almost the same position in the space of separation parameters. Based on this property, if an initial separation matrix for a learning process in a frequency bin is chosen equal to the final separation matrix of the learning process in the neighboring frequency bin, the learning process automatically leads us to separated signals with the same permutation as that of the neighbor frequency bin. In each bin, but except the starting one, by chosen the initial separation matrix in such a way, the permutation problem in the time domain reconstruction can be avoided. We present the results of some simulations and experiments on both artificially synthesized speech data and real‐world speech data, which show the effectiveness of our approach.

Autonomous signal separation microphone system based on the spatio-temporal gradient analysis

This paper presents a novel autonomous directivity microphone system based on the newly proposed spatio-temporal blind source separation. Recently, the methods of blind source separation and multi-deconvolution of source signals have been proposed in various fields, especially, acoustic applications including the cocktail-party problem. The blind source separation principally uses no a priori knowledge about parameters of convolution, filtering and mixing. In the simplest case of the blind source separation problems, observed mixed signals are linear combinations of unknown mutually statistically independent, zero-mean source signals. The spatio-temporal blind signal separation algorithm utilizes the linearity among the four signals: (1) temporal gradient, (2) x; (3) y; and (4) z-directional spatial gradients of the sound-pressure, all of which are governed by the equation of advection. The proposed method, therefore, has an ability to simplify the convolution blind source separation problems into the instantaneous blind source separation over the spatio-temporal gradient space. The acoustical experiments are performed with the particle velocity microphone (Microflown) successfully instead of sound pressure microphones. Because, x; y; and z-directional gradients of the sound pressure are equivalent the temporal derivatives of the corresponding directional particle velocities theoretically.

A fast fixed-point algorithm for complexity pursuit

Complexity pursuit is a recently developed algorithm using the gradient descent for separating interesting components from time series. It is an extension of projection pursuit to time series data and the method is closely related to blind separation of time-dependent source signals and independent component analysis (ICA). In this paper, a fixed-point algorithm for complexity pursuit is introduced. The fixed-point algorithm inherits the advantages of the well-known FastICA algorithm in ICA, which is very simple, converges fast, and does not need choose any learning step sizes.

Nonlinear blind source separation using a hybrid RBF-FMLP network

A novel scheme for blind source separation of nonlinearly mixed signals is developed using a hybrid system based on radial basis function (RBF) and feedforward multilayer perceptron (FMLP) networks. In this paper, the development of the proposed RBF-FMLP network is discussed, which hinges on the theory of nonlinear regularisation. The proposed network uses simultaneously local and global mapping bases to perform both signal separation and reconstruction of continuous signals in addition to signals that exhibit a high degree of fluctuation. The parameters of the proposed system are estimated jointly using the generalised gradient descent approach thereby rendering the training process relatively simple and efficient in computation. Simulations of both synthetic and speech signals have been undertaken to verify the efficacy of the proposed scheme in terms of speed, accuracy and robustness against noise.

Using skew Gabor filter in source signal separation and local spectral orientation analysis

Responses of Gabor wavelets in the mid-frequency space build a local spectral representation scheme with optimal properties regarding the time-frequency uncertainty principle. However, when using Gabor wavelets we observe a skewness in the mid-frequency space caused by the unsymmetrically spreading effect of Gabor wavelets. Though in most current applications the skewness does not obstruct the sampling of the spectral domain, it affects the identification and separation of source Signals from the filter response in the mid-frequency space. In this paper, we present a modification of the original Gabor filter, the skew Gabor filter, which corrects skewness so that the filter response can be described with a sum-of-Gaussians model in the mid-frequency space. The correction further enables us to use higher order moment information to analytically separate different source signal components. This provides us with an elegant framework to de-blur the filter response which is not characterized by the limited spectral resolution of other local spectral representations.

Blind source separation of noisy harmonic signals for rotating machine diagnosis

Blind source separation (BSS) consists of recovering signals from different physical sources from several observed combinations independently of the propagation medium. BSS is also a promising tool for non-destructive machine condition monitoring by vibration analysis, as it is intended to retrieve the signature of a single rotating machine from combinations of several working machines. In this way, BSS can be seen as a pre-processing step that improves the diagnosis. BSS methods generally assume observations that are either noise-free or corrupted with spatially distinct white noises. In the latter case, principal component analysis (PCA) is applied as a first step to filter out the noise and whiten the observations. Obviously, the efficiency of the whole separation procedure depends on the accuracy of the first step (PCA). However, in the real world, signals of rotating machine vibration may be severely corrupted with spatially correlated noises and therefore the signal subspace will not be correctly estimated with PCA. The purpose of this paper is to propose a ‘robust-to-noise’ technique for the separation of rotating machine signals. The sources are assumed here to be periodic and so can be modelled as the sum of sinusoids of harmonic frequencies. A new estimator of the signal subspace and the whitening matrix is introduced which exploits the model of sinusoidal sources and uses spectral matrices of delayed observations to eliminate the influence of the noise. After whitening, the second step of source separation remains unchanged. Finally, performance of the algorithm is investigated with artificial data and experimental rotating machine vibration data.

GABA Is Involved in Spatial Unmasking in the Frog Auditory Midbrain

Real-world listening situations comprise multiple auditory objects. Sounds originating from different objects are summated at the eardrum. The auditory system therefore must segregate the streams of sounds associated with the different objects. One listening strategy in complex environments is to attend to signals originating from one spatial location. In doing so, signal detection is compromised when a masker is present at close proximity, and detection is improved if the masker is spatially separated from the signal. A recent study has shown that, in frogs, spatial unmasking is more robust at the midbrain than at the periphery, indicating the importance of central mechanisms for this process. In this study, we investigated spatial unmasking patterns of single neurons in the frog inferior colliculus (IC) before and during iontophoretic application of bicuculline, a GABA(A) receptor antagonist. We found that drug application markedly decreased the strength of spatial unmasking such that even large angular separation of signal and masker sources produced only a weak masking release. Under the drug, the strength of spatial unmasking of midbrain neurons approximated that of auditory nerve fibers. These data show that GABAergic interactions in the auditory midbrain play an important role in spatial unmasking. Analysis of the effect of the drug on the direction sensitivity of the units shows that for the majority of IC units, bicuculline degrades binaural processing involved in directional coding, thereby compromising spatial unmasking. For other IC units, however, the decline in the strength of spatial unmasking is attributable to the effects of bicuculline on different central auditory processes.

Criterion for Blind Signals Separation Based on Correlation Function

Blind separation of source signals usually relies either on the condition of statistically independence or involving their higher-order cumulants. The model of two channels signal separation is considered. A criterion based on correlation functions is proposed. It is proved that the signals can be separated, using only the condition of noncorrelation. An algorithm is derived, which only involves the solution to quadric nonlinear equations.

Blind source separation of signals with known alphabets using /spl epsi/-approximation algorithms

We show that blind separation of signals in given alphabets can be formulated into a quadratic optimization problem with integer constraints. Then, efficient /spl epsi/-approximation algorithms are applied to directly estimate the transmitted signals. The proposed approach does not require any high order statistics. Moreover, the algorithms converge to an /spl epsi/ neighborhood of the global optimum with polynomial computational complexity. Simulations show that the algorithm achieves satisfactory performance using a short length of data.

Second-order statistics based blind source separation using a bank of subband filters

This paper presents a novel approach to blind source separation of narrowband signals in additive either white (i.e., time-uncorrelated) noise or colored (i.e., time-correlated) noise of which the frequencies of its spectral peaks are either known or can be estimated. The main idea behind this approach is that a signal vector can be decomposed into a set of subband signal vectors in order to separate the spectra of the signals of interest from the noise spectra. It is shown that the subband technique can provide an unbiased estimate of the second-order statistics of a noisy observed signal vector. The proposed blind source separation algorithm is developed: (1) by whitening the noisy observed signal vector using the eigenvalue decomposition (EVD) of an unbiased estimate of the zero time-lag correlation matrix computed on the basis of the subband signals; and (2) by applying the joint approximate diagonalization (JAD) on a new proposed set of time-lag correlation matrices of the whitened signal vector. In this set, each correlation matrix of the whitened signal vector at certain time-lag is decomposed into a subset of the correlation matrices between the whitened signal vector and its subband vectors. This is motivated by the capability of separating and then omitting the cross-correlation matrices belonging to the subbands of the colored noise from the set. Simulation results using computer-generated signals, real-world speech and real-world biomedical signals confirm the high efficiency and usefulness of the proposed approach.

Blind source separation technique for reduction of co-channel interference

A technique for co-channel interference reduction that uses blind separation of source signals through independent component analysis (ICA) is given. An outline of an ICA-based BPSK receiver operating in a flat non-dispersive channel is presented. The performance of the receiver is evaluated through computer simulations which demonstrate the significant improvement of the receiver performance.

Robust blind source separation algorithms using cumulants

In this paper we propose a new approach to blind separation of independent source signals that, while avoiding the imposition of an orthogonal mixing matrix, is robust with respect to the existence of additive Gaussian noise in the mixture. We demonstrate that, for the wide class of source distributions with certain non-null cumulants and a pre-specified scaling, separation is always a saddle point of a cumulant-based cost function. We propose a quasi-Newton approach for determining this saddle point. This enables us to obtain a family of separation algorithms which, based on higher order statistics, yields unbiased estimates even in the presence of large Gaussian noise and has the interesting property of local isotropic convergence. Another family of algorithms that incorporates second-order statistics loses the former desirable convergence properties but it provides more precise estimates in the absence of noise. Extensive computer simulations confirm robustness and the excellent performance of the resulting algorithms.

Effect of signal length on the performance of independent component analysis when extracting the lambda wave.

The aim of the study was to investigate the effect of signal length on the performance of a signal source separation method, independent component analysis (ICA), when extracting the visual evoked potential (EP) lambda wave from saccade-related electro-encephalogram (EEG) waveforms. A method was devised that enabled the effective length of the recorded EEG traces to be increased prior to processing by ICA. This involved abutting EEG traces from an appropriate number of successive trials (a trial was a set of waveforms recorded from 64 electrode locations in a study investigating saccade performance). ICA was applied to the saccade-related EEG and electro-oculogram (EOG) waveforms recorded from the electrode locations. One spatial and five temporal features of the lambda wave were monitored to assess the performance of ICA applied to both abutted and non-abutted waveforms. ICA applied to abutted trials managed to extract all six features across all seven subjects included in the study. This was not the case when ICA was applied to the non-abutted trials. It was quantitatively demonstrated that the process of abutting EEG waveforms was useful for ICA preprocessing when extracting lambda waves.

Complex-Weighted One-Unit ‘Rigid-Bodies’ Learning Rule for Independent Component Analysis

Over the recent years, noticeable theoretical efforts have been devoted to the understanding of the role of networks' parameter spaces in neural learning. One of the contributions in this field concerns the study of weight-flows on Stiefel manifold, which is the natural parameter-space's algebraic-structure in some unsupervised (information-theoretic) learning task. An algorithm belonging to the class of learning equations generating Stiefel-flows is based on the ‘rigid-body’ theory, introduced by the present Author in 1996. The aim of this Letter is to present an investigation on the capability of a complex-weighted neuron, trained by a ‘rigid-bodies’ learning theory, with application to blind source separation of complex-valued independent signals for telecommunication systems.

An approach to blind source separation based on temporal structure of speech signals

In this paper, we introduce a new technique for blind source separation of speech signals. We focus on the temporal structure of the signals. The idea is to apply the decorrelation method proposed by Molgedey and Schuster in the time–frequency domain. Since we are applying separation algorithm on each frequency separately, we have to solve the amplitude and permutation ambiguity properly to reconstruct the separated signals. For solving the amplitude ambiguity, we use the matrix inversion and for the permutation ambiguity, we introduce a method based on the temporal structure of speech signals. We show some results of experiments with both artificially controlled data and speech data recorded in the real environment.

Signal Source Separation in the Analysis of Neural Activity in Brain

This research examines the spatial and temporal characteristics of the responses to stimulation of the barrel cortex in anesthetized rats using optical imaging with particular emphasis on methods of analysis which reduce the effects of low-frequency oscillations on localization of the activated cortical region. Image sequences were captured using a light source with a narrow bandwidth of wavelength (590 ± 2 nm). On each trial image data were collected at 15 Hz and stored over a 12-s period starting 8 s before stimulation onset. Stimulation was for 1 s using an oscillating whisker vibrator (∼1-mm deflection at 5 Hz). For each subject a total of 30 experimental trials were collected and averaged. There was an interstimulus interval of 26 s. The trial-averaged data were analyzed using two related signal source separation algorithms. Both algorithms use a weak model of the expected temporal response as a filter to exclude contributions from low-frequency baseline oscillations which we call the V-signal. We found that both algorithms successfully separated most of the effects of the V-signal from the response to the stimulation. The performance of the algorithms compared favorably with the performance of related algorithms without weak constraints and the “ratio of means” strategy used by C. H. Chen-Bee et al. (1996b, J. Neurosci. Methods 68:28–37; C. H. Chen-Bee et al., 2000, J. Neurosci. Methods 97:157–173).

Blind source separation by nonstationarity of variance: a cumulant-based approach

Blind separation of source signals usually relies either on the nonGaussianity of the signals or on their linear autocorrelations. A third approach was introduced by Matsuoka et al. (1995), who showed that source separation can be performed by using the nonstationarity of the signals, in particular the nonstationarity of their variances. In this paper, we show how to interpret the nonstationarity due to a smoothly changing variance in terms of higher order cross-cumulants. This is based on the time-correlation of the squares (energies) of the signals and leads to a simple optimization criterion. Using this criterion, we construct a fixed-point algorithm that is computationally very efficient.

Convolutive blind source separation of speech signals based on amplitude modulation decorrelation

The problem of blind separation of a convolutive mixture of speech signals is considered. Signal separation is performed in the frequency domain. The amplitude modulation decorrelation algorithm for convolutive blind source separation of speech is described, the first ideas of which were presented by Anemüller at the joint ASA/EAA/DAGA meeting, Berlin, 1999. The algorithm is based on the fact that the frequency-specific envelopes of speech signals exhibit correlation across different frequencies. This feature can be used to solve the ‘‘permutation problem’’ of frequency-domain-based blind source separation algorithms. Furthermore, it leads to separation of good quality since it results in a high number of constraints which must be fulfilled by the unmixed signals. Results for the separation of speech signals are presented for different mixing scenarios, including real-room reverberant mixing.