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

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.

Blind channel deconvolution of real world signals using source separation techniques

In this paper we present a method for blind deconvolution of linear channels based on source separation techniques, for real word signals. This technique applied to blind deconvolution problems is based in exploiting not the spatial independence between signals but the temporal independence between samples of the signal. Our objective is to minimize the mutual information between samples of the output in order to retrieve the original signal. In order to make use of use this idea the input signal must be a non-Gaussian i.i.d. signal. Because most real world signals do not have this i.i.d. nature, we will need to preprocess the original signal before the transmission into the channel. Likewise we should assure that the transmitted signal has non-Gaussian statistics in order to achieve the correct function of the algorithm. The strategy used for this preprocessing will be presented in this paper. If the receiver has the inverse of the preprocess, the original signal can be reconstructed without the convolutive distortion.

Source separation techniques applied to linear prediction

The prediction filters are well known models for signal estimation, in communications, control and many others areas. The classical method for deriving linear prediction coding (LPC) filters is often based on the minimization of a mean square error (MSE). Consequently, second order statistics are only required, but the estimation is only optimal if the residue is independent and identically distributed (iid) Gaussian. In this paper, we derive the ML estimate of the prediction filter. Relationships with robust estimation of auto-regressive (AR) processes, with blind deconvolution and with source separation based on mutual information minimization are then detailed. The algorithm, based on the minimization of a high-order statistics criterion, uses on-line estimation of the residue statistics. Experimental results emphasize on the interest of this approach.

Unmixing hyperspectral data: independent and dependent component analysis

The development of high spatial resolution airborne and spaceborne sensors has improved the capability of ground-based data collection in the fields of agriculture, geography, geology, mineral identification, detection [2, 3], and classification [4–8]. The signal read by the sensor from a given spatial element of resolution and at a given spectral band is a mixing of components originated by the constituent substances, termed endmembers, located at that element of resolution. This chapter addresses hyperspectral unmixing, which is the decomposition of the pixel spectra into a collection of constituent spectra, or spectral signatures, and their corresponding fractional abundances indicating the proportion of each endmember present in the pixel [9, 10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. The linear mixing model holds when the mixing scale is macroscopic [13]. The nonlinear model holds when the mixing scale is microscopic (i.e., intimate mixtures) [14, 15]. The linear model assumes negligible interaction among distinct endmembers [16, 17]. The nonlinear model assumes that incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [18]. Under the linear mixing model and assuming that the number of endmembers and their spectral signatures are known, hyperspectral unmixing is a linear problem, which can be addressed, for example, under the maximum likelihood setup [19], the constrained least-squares approach [20], the spectral signature matching [21], the spectral angle mapper [22], and the subspace projection methods [20, 23, 24]. Orthogonal subspace projection [23] reduces the data dimensionality, suppresses undesired spectral signatures, and detects the presence of a spectral signature of interest. The basic concept is to project each pixel onto a subspace that is orthogonal to the undesired signatures. As shown in Settle [19], the orthogonal subspace projection technique is equivalent to the maximum likelihood estimator. This projection technique was extended by three unconstrained least-squares approaches [24] (signature space orthogonal projection, oblique subspace projection, target signature space orthogonal projection). Other works using maximum a posteriori probability (MAP) framework [25] and projection pursuit [26, 27] have also been applied to hyperspectral data. In most cases the number of endmembers and their signatures are not known. Independent component analysis (ICA) is an unsupervised source separation process that has been applied with success to blind source separation, to feature extraction, and to unsupervised recognition [28, 29]. ICA consists in finding a linear decomposition of observed data yielding statistically independent components. Given that hyperspectral data are, in given circumstances, linear mixtures, ICA comes to mind as a possible tool to unmix this class of data. In fact, the application of ICA to hyperspectral data has been proposed in reference 30, where endmember signatures are treated as sources and the mixing matrix is composed by the abundance fractions, and in references 9, 25, and 31–38, where sources are the abundance fractions of each endmember. In the first approach, we face two problems: (1) The number of samples are limited to the number of channels and (2) the process of pixel selection, playing the role of mixed sources, is not straightforward. In the second approach, ICA is based on the assumption of mutually independent sources, which is not the case of hyperspectral data, since the sum of the abundance fractions is constant, implying dependence among abundances. This dependence compromises ICA applicability to hyperspectral images. In addition, hyperspectral data are immersed in noise, which degrades the ICA performance. IFA [39] was introduced as a method for recovering independent hidden sources from their observed noisy mixtures. IFA implements two steps. First, source densities and noise covariance are estimated from the observed data by maximum likelihood. Second, sources are reconstructed by an optimal nonlinear estimator. Although IFA is a well-suited technique to unmix independent sources under noisy observations, the dependence among abundance fractions in hyperspectral imagery compromises, as in the ICA case, the IFA performance. Considering the linear mixing model, hyperspectral observations are in a simplex whose vertices correspond to the endmembers. Several approaches [40–43] have exploited this geometric feature of hyperspectral mixtures [42]. Minimum volume transform (MVT) algorithm [43] determines the simplex of minimum volume containing the data. The MVT-type approaches are complex from the computational point of view. Usually, these algorithms first find the convex hull defined by the observed data and then fit a minimum volume simplex to it. Aiming at a lower computational complexity, some algorithms such as the vertex component analysis (VCA) [44], the pixel purity index (PPI) [42], and the N-FINDR [45] still find the minimum volume simplex containing the data cloud, but they assume the presence in the data of at least one pure pixel of each endmember. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. Hyperspectral sensors collects spatial images over many narrow contiguous bands, yielding large amounts of data. For this reason, very often, the processing of hyperspectral data, included unmixing, is preceded by a dimensionality reduction step to reduce computational complexity and to improve the signal-to-noise ratio (SNR). Principal component analysis (PCA) [46], maximum noise fraction (MNF) [47], and singular value decomposition (SVD) [48] are three well-known projection techniques widely used in remote sensing in general and in unmixing in particular. The newly introduced method [49] exploits the structure of hyperspectral mixtures, namely the fact that spectral vectors are nonnegative. The computational complexity associated with these techniques is an obstacle to real-time implementations. To overcome this problem, band selection [50] and non-statistical [51] algorithms have been introduced. This chapter addresses hyperspectral data source dependence and its impact on ICA and IFA performances. The study consider simulated and real data and is based on mutual information minimization. Hyperspectral observations are described by a generative model. This model takes into account the degradation mechanisms normally found in hyperspectral applications—namely, signature variability [52–54], abundance constraints, topography modulation, and system noise. The computation of mutual information is based on fitting mixtures of Gaussians (MOG) to data. The MOG parameters (number of components, means, covariances, and weights) are inferred using the minimum description length (MDL) based algorithm [55]. We study the behavior of the mutual information as a function of the unmixing matrix. The conclusion is that the unmixing matrix minimizing the mutual information might be very far from the true one. Nevertheless, some abundance fractions might be well separated, mainly in the presence of strong signature variability, a large number of endmembers, and high SNR. We end this chapter by sketching a new methodology to blindly unmix hyperspectral data, where abundance fractions are modeled as a mixture of Dirichlet sources. This model enforces positivity and constant sum sources (full additivity) constraints. The mixing matrix is inferred by an expectation-maximization (EM)-type algorithm. This approach is in the vein of references 39 and 56, replacing independent sources represented by MOG with mixture of Dirichlet sources. Compared with the geometric-based approaches, the advantage of this model is that there is no need to have pure pixels in the observations. The chapter is organized as follows. Section 6.2 presents a spectral radiance model and formulates the spectral unmixing as a linear problem accounting for abundance constraints, signature variability, topography modulation, and system noise. Section 6.3 presents a brief resume of ICA and IFA algorithms. Section 6.4 illustrates the performance of IFA and of some well-known ICA algorithms with experimental data. Section 6.5 studies the ICA and IFA limitations in unmixing hyperspectral data. Section 6.6 presents results of ICA based on real data. Section 6.7 describes the new blind unmixing scheme and some illustrative examples. Section 6.8 concludes with some remarks.

Parametric Approach to Blind Deconvolution of Nonlinear Channels

A parametric procedure for the blind inversion of nonlinear channels is proposed, based on a recent method of blind source separation in nonlinear mixtures. Experiments show that the proposed algorithms perform efficiently, even in the presence of hard distortion. The method, based on the minimization of the output mutual information, needs the knowledge of log-derivative of input distribution (the so-called score function). Each algorithm consists of three adaptive blocks: one devoted to adaptive estimation of the score function, and two other blocks estimating the inverses of the linear and nonlinear parts of the channel, (quasi-)optimally adapted using the estimated score functions. This paper is mainly concerned by the nonlinear part, for which we propose two parametric models, the first based on a polynomial model and the second on a neural network, while [14, 15] proposed non-parametric approaches.

Quasi-Nonparametric Blind Inversion of Wiener Systems

An e cient procedure for the blind inversion of a nonlinear Wiener system is proposed. We proved that the problem can be expressed as a problem of blind source separation in nonlinear mixtures, for which a solution has been recently proposed. Based on a quasi-nonparametric relative gradient descent, the proposed algorithm can perform e ciently even in the presence of hard distortions.

A semi-blind reception scheme based on ICA for multiuser MIMO-STBC system

When the orthogonal space-time block code (STBC), or the Alamouti code, is applied on a multiple-input multiple-output (MIMO) communications system, the optimum reception can be achieved by a simple signal decoupling at the receiver. The performance, however, deteriorates significantly in presence of co-channel interference (CCI) from other users. In this paper, such CCI problem is overcome by applying the independent component analysis (ICA), a blind source separation algorithm. This is based on the fact that, if the transmission data from every transmit antenna are mutually independent, they can be effectively separated at the receiver with the principle of the blind source separation. Then equivalently, the CCI is suppressed. Although they are not required by the ICA algorithm itself, a small number of training data are necessary to eliminate the phase and order ambiguities at the ICA outputs, leading to a semi-blind approach. Numerical simulation is also shown to verify the proposed ICA approach in the multiuser MIMO system.

Source separation collection and processing equipment : final report.

"January 1981"--Cover.

Source separation : the community awareness program in Somerville and Marblehead, Massachusetts /

Mode of access: Internet.

Multimaterial source separation in Marblehead and Somerville, Massachusetts /

December 1979.

Managing the waste stream : background information for planning source separation programs : final report /

"Printed: July 1989."