274 research outputs found
Spatiotemporal Analysis of Multichannel EEG: CARTOOL
This paper describes methods to analyze the brain's electric fields recorded with multichannel Electroencephalogram (EEG) and demonstrates their implementation in the software CARTOOL. It focuses on the analysis of the spatial properties of these fields and on quantitative assessment of changes of field topographies across time, experimental conditions, or populations. Topographic analyses are advantageous because they are reference independents and thus render statistically unambiguous results. Neurophysiologically, differences in topography directly indicate changes in the configuration of the active neuronal sources in the brain. We describe global measures of field strength and field similarities, temporal segmentation based on topographic variations, topographic analysis in the frequency domain, topographic statistical analysis, and source imaging based on distributed inverse solutions. All analysis methods are implemented in a freely available academic software package called CARTOOL. Besides providing these analysis tools, CARTOOL is particularly designed to visualize the data and the analysis results using 3-dimensional display routines that allow rapid manipulation and animation of 3D images. CARTOOL therefore is a helpful tool for researchers as well as for clinicians to interpret multichannel EEG and evoked potentials in a global, comprehensive, and unambiguous way
Detecting single-trial EEG evoked potential using a wavelet domain linear mixed model: application to error potentials classification
Objective. The main goal of this work is to develop a model for multi-sensor
signals such as MEG or EEG signals, that accounts for the inter-trial
variability, suitable for corresponding binary classification problems. An
important constraint is that the model be simple enough to handle small size
and unbalanced datasets, as often encountered in BCI type experiments.
Approach. The method involves linear mixed effects statistical model, wavelet
transform and spatial filtering, and aims at the characterization of localized
discriminant features in multi-sensor signals. After discrete wavelet transform
and spatial filtering, a projection onto the relevant wavelet and spatial
channels subspaces is used for dimension reduction. The projected signals are
then decomposed as the sum of a signal of interest (i.e. discriminant) and
background noise, using a very simple Gaussian linear mixed model. Main
results. Thanks to the simplicity of the model, the corresponding parameter
estimation problem is simplified. Robust estimates of class-covariance matrices
are obtained from small sample sizes and an effective Bayes plug-in classifier
is derived. The approach is applied to the detection of error potentials in
multichannel EEG data, in a very unbalanced situation (detection of rare
events). Classification results prove the relevance of the proposed approach in
such a context. Significance. The combination of linear mixed model, wavelet
transform and spatial filtering for EEG classification is, to the best of our
knowledge, an original approach, which is proven to be effective. This paper
improves on earlier results on similar problems, and the three main ingredients
all play an important role
Martian time-series unraveled: A multi-scale nested approach with factorial variational autoencoders
Unsupervised source separation involves unraveling an unknown set of source
signals recorded through a mixing operator, with limited prior knowledge about
the sources, and only access to a dataset of signal mixtures. This problem is
inherently ill-posed and is further challenged by the variety of time-scales
exhibited by sources in time series data. Existing methods typically rely on a
preselected window size that limits their capacity to handle multi-scale
sources. To address this issue, instead of operating in the time domain, we
propose an unsupervised multi-scale clustering and source separation framework
by leveraging wavelet scattering covariances that provide a low-dimensional
representation of stochastic processes, capable of distinguishing between
different non-Gaussian stochastic processes. Nested within this representation
space, we develop a factorial Gaussian-mixture variational autoencoder that is
trained to (1) probabilistically cluster sources at different time-scales and
(2) independently sample scattering covariance representations associated with
each cluster. Using samples from each cluster as prior information, we
formulate source separation as an optimization problem in the wavelet
scattering covariance representation space, resulting in separated sources in
the time domain. When applied to seismic data recorded during the NASA InSight
mission on Mars, our multi-scale nested approach proves to be a powerful tool
for discriminating between sources varying greatly in time-scale, e.g.,
minute-long transient one-sided pulses (known as ``glitches'') and structured
ambient noises resulting from atmospheric activities that typically last for
tens of minutes. These results provide an opportunity to conduct further
investigations into the isolated sources related to atmospheric-surface
interactions, thermal relaxations, and other complex phenomena
Locally Most Powerful Invariant Tests for Correlation and Sphericity of Gaussian Vectors
In this paper we study the existence of locally most powerful invariant tests
(LMPIT) for the problem of testing the covariance structure of a set of
Gaussian random vectors. The LMPIT is the optimal test for the case of close
hypotheses, among those satisfying the invariances of the problem, and in
practical scenarios can provide better performance than the typically used
generalized likelihood ratio test (GLRT). The derivation of the LMPIT usually
requires one to find the maximal invariant statistic for the detection problem
and then derive its distribution under both hypotheses, which in general is a
rather involved procedure. As an alternative, Wijsman's theorem provides the
ratio of the maximal invariant densities without even finding an explicit
expression for the maximal invariant. We first consider the problem of testing
whether a set of -dimensional Gaussian random vectors are uncorrelated or
not, and show that the LMPIT is given by the Frobenius norm of the sample
coherence matrix. Second, we study the case in which the vectors under the null
hypothesis are uncorrelated and identically distributed, that is, the
sphericity test for Gaussian vectors, for which we show that the LMPIT is given
by the Frobenius norm of a normalized version of the sample covariance matrix.
Finally, some numerical examples illustrate the performance of the proposed
tests, which provide better results than their GLRT counterparts
Sensor array signal processing : two decades later
Caption title.Includes bibliographical references (p. 55-65).Supported by Army Research Office. DAAL03-92-G-115 Supported by the Air Force Office of Scientific Research. F49620-92-J-2002 Supported by the National Science Foundation. MIP-9015281 Supported by the ONR. N00014-91-J-1967 Supported by the AFOSR. F49620-93-1-0102Hamid Krim, Mats Viberg
Asymptotic regime for impropriety tests of complex random vectors
Impropriety testing for complex-valued vector has been considered lately due
to potential applications ranging from digital communications to complex media
imaging. This paper provides new results for such tests in the asymptotic
regime, i.e. when the vector dimension and sample size grow commensurately to
infinity. The studied tests are based on invariant statistics named impropriety
coefficients. Limiting distributions for these statistics are derived, together
with those of the Generalized Likelihood Ratio Test (GLRT) and Roy's test, in
the Gaussian case. This characterization in the asymptotic regime allows also
to identify a phase transition in Roy's test with potential application in
detection of complex-valued low-rank subspace corrupted by proper noise in
large datasets. Simulations illustrate the accuracy of the proposed asymptotic
approximations.Comment: 11 pages, 8 figures, submitted to IEEE TS
Asymptotically Optimal Blind Calibration of Uniform Linear Sensor Arrays for Narrowband Gaussian Signals
An asymptotically optimal blind calibration scheme of uniform linear arrays
for narrowband Gaussian signals is proposed. Rather than taking the direct
Maximum Likelihood (ML) approach for joint estimation of all the unknown model
parameters, which leads to a multi-dimensional optimization problem with no
closed-form solution, we revisit Paulraj and Kailath's (P-K's) classical
approach in exploiting the special (Toeplitz) structure of the observations'
covariance. However, we offer a substantial improvement over P-K's ordinary
Least Squares (LS) estimates by using asymptotic approximations in order to
obtain simple, non-iterative, (quasi-)linear Optimally-Weighted LS (OWLS)
estimates of the sensors gains and phases offsets with asymptotically optimal
weighting, based only on the empirical covariance matrix of the measurements.
Moreover, we prove that our resulting estimates are also asymptotically optimal
w.r.t. the raw data, and can therefore be deemed equivalent to the ML Estimates
(MLE), which are otherwise obtained by joint ML estimation of all the unknown
model parameters. After deriving computationally convenient expressions of the
respective Cram\'er-Rao lower bounds, we also show that our estimates offer
improved performance when applied to non-Gaussian signals (and/or noise) as
quasi-MLE in a similar setting. The optimal performance of our estimates is
demonstrated in simulation experiments, with a considerable improvement
(reaching an order of magnitude and more) in the resulting mean squared errors
w.r.t. P-K's ordinary LS estimates. We also demonstrate the improved accuracy
in a multiple-sources directions-of-arrivals estimation task.Comment: in IEEE Transactions on Signal Processin
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