7,889 research outputs found

    Regularized Covariance Matrix Estimation in Complex Elliptically Symmetric Distributions Using the Expected Likelihood Approach - Part 1: The Over-Sampled Case

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    In \cite{Abramovich04}, it was demonstrated that the likelihood ratio (LR) for multivariate complex Gaussian distribution has the invariance property that can be exploited in many applications. Specifically, the probability density function (p.d.f.) of this LR for the (unknown) actual covariance matrix R0\R_{0} does not depend on this matrix and is fully specified by the matrix dimension MM and the number of independent training samples TT. Since this p.d.f. could therefore be pre-calculated for any a priori known (M,T)(M,T), one gets a possibility to compare the LR of any derived covariance matrix estimate against this p.d.f., and eventually get an estimate that is statistically ``as likely'' as the a priori unknown actual covariance matrix. This ``expected likelihood'' (EL) quality assessment allows for significant improvement of MUSIC DOA estimation performance in the so-called ``threshold area'' \cite{Abramovich04,Abramovich07d}, and for diagonal loading and TVAR model order selection in adaptive detectors \cite{Abramovich07,Abramovich07b}. Recently, a broad class of the so-called complex elliptically symmetric (CES) distributions has been introduced for description of highly in-homogeneous clutter returns. The aim of this series of two papers is to extend the EL approach to this class of CES distributions as well as to a particularly important derivative of CES, namely the complex angular central distribution (ACG). For both cases, we demonstrate a similar invariance property for the LR associated with the true scatter matrix \mSigma_{0}. Furthermore, we derive fixed point regularized covariance matrix estimates using the generalized expected likelihood methodology. This first part is devoted to the conventional scenario (T≥MT \geq M) while Part 2 deals with the under-sampled scenario (T≤MT \leq M)

    Regularized Nonparametric Volterra Kernel Estimation

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    In this paper, the regularization approach introduced recently for nonparametric estimation of linear systems is extended to the estimation of nonlinear systems modelled as Volterra series. The kernels of order higher than one, representing higher dimensional impulse responses in the series, are considered to be realizations of multidimensional Gaussian processes. Based on this, prior information about the structure of the Volterra kernel is introduced via an appropriate penalization term in the least squares cost function. It is shown that the proposed method is able to deliver accurate estimates of the Volterra kernels even in the case of a small amount of data points

    Regularized adaptive long autoregressive spectral analysis

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    This paper is devoted to adaptive long autoregressive spectral analysis when (i) very few data are available, (ii) information does exist beforehand concerning the spectral smoothness and time continuity of the analyzed signals. The contribution is founded on two papers by Kitagawa and Gersch. The first one deals with spectral smoothness, in the regularization framework, while the second one is devoted to time continuity, in the Kalman formalism. The present paper proposes an original synthesis of the two contributions: a new regularized criterion is introduced that takes both information into account. The criterion is efficiently optimized by a Kalman smoother. One of the major features of the method is that it is entirely unsupervised: the problem of automatically adjusting the hyperparameters that balance data-based versus prior-based information is solved by maximum likelihood. The improvement is quantified in the field of meteorological radar

    Neural Connectivity with Hidden Gaussian Graphical State-Model

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    The noninvasive procedures for neural connectivity are under questioning. Theoretical models sustain that the electromagnetic field registered at external sensors is elicited by currents at neural space. Nevertheless, what we observe at the sensor space is a superposition of projected fields, from the whole gray-matter. This is the reason for a major pitfall of noninvasive Electrophysiology methods: distorted reconstruction of neural activity and its connectivity or leakage. It has been proven that current methods produce incorrect connectomes. Somewhat related to the incorrect connectivity modelling, they disregard either Systems Theory and Bayesian Information Theory. We introduce a new formalism that attains for it, Hidden Gaussian Graphical State-Model (HIGGS). A neural Gaussian Graphical Model (GGM) hidden by the observation equation of Magneto-encephalographic (MEEG) signals. HIGGS is equivalent to a frequency domain Linear State Space Model (LSSM) but with sparse connectivity prior. The mathematical contribution here is the theory for high-dimensional and frequency-domain HIGGS solvers. We demonstrate that HIGGS can attenuate the leakage effect in the most critical case: the distortion EEG signal due to head volume conduction heterogeneities. Its application in EEG is illustrated with retrieved connectivity patterns from human Steady State Visual Evoked Potentials (SSVEP). We provide for the first time confirmatory evidence for noninvasive procedures of neural connectivity: concurrent EEG and Electrocorticography (ECoG) recordings on monkey. Open source packages are freely available online, to reproduce the results presented in this paper and to analyze external MEEG databases

    Joint deprojection of Sunyaev-Zeldovich and X-ray images of galaxy clusters

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    We present two non-parametric deprojection methods aimed at recovering the three-dimensional density and temperature profiles of galaxy clusters from spatially resolved thermal Sunyaev-Zeldovich (tSZ) and X-ray surface brightness maps, thus avoiding the use of X-ray spectroscopic data. In both methods, clusters are assumed to be spherically symmetric and modeled with an onion-skin structure. The first method follows a direct geometrical approach. The second method is based on the maximization of a single joint (tSZ and X-ray) likelihood function, which allows one to fit simultaneously the two signals by following a Monte Carlo Markov Chain approach. These techniques are tested against a set of cosmological simulations of clusters, with and without instrumental noise. We project each cluster along the three orthogonal directions defined by the principal axes of the momentum of inertia tensor. This enables us to check any bias in the deprojection associated to the cluster elongation along the line of sight. After averaging over all the three projection directions, we find an overall good reconstruction, with a small (<~10 per cent) overestimate of the gas density profile. This turns into a comparable overestimate of the gas mass within the virial radius, which we ascribe to the presence of residual gas clumping. Apart from this small bias the reconstruction has an intrinsic scatter of about 5 per cent, which is dominated by gas clumpiness. Cluster elongation along the line of sight biases the deprojected temperature profile upwards at r<~0.2r_vir and downwards at larger radii. A comparable bias is also found in the deprojected temperature profile. Overall, this turns into a systematic underestimate of the gas mass, up to 10 percent. (Abridged)Comment: 17 pages, 15 figures, accepted by MNRA
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