20 research outputs found

    Squared-loss mutual information via high-dimension coherence matrix estimation

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    Squared-loss mutual information (SMI) is a surro- gate of Shannon mutual information that is more advantageous for estimation. On the other hand, the coherence matrix of a pair of random vectors, a power-normalized version of the sample cross-covariance matrix, is a well-known second-order statistic found in the core of fundamental signal processing problems, such as canonical correlation analysis (CCA). This paper shows that SMI can be estimated from a pair of independent and identically distributed (i.i.d.) samples as a squared Frobenius norm of a coherence matrix estimated after mapping the data onto some fixed feature space. Moreover, low computation complexity is achieved through the fast Fourier transform (FFT) by exploiting the Toeplitz structure of the involved autocorrelation matrices in that space. The performance of the method is analyzed via computer simulations using Gaussian mixture models.This work is supported by projects TEC2016-76409-C2-1-R (WINTER), Ministerio de Economia y Competividad, Spanish National Research Plan, and 2017 SGR 578 - AGAUR, Catalan Government.Peer ReviewedPostprint (published version

    A novel formulation of independence detection based on the sample characteristic function

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    A novel independence test for continuous random sequences is proposed in this paper. The test is based on seeking for coherence in a particular fixed-dimension feature space based on a uniform sampling of the sample characteristic function of the data, providing significant computational advantages over kernel methods. This feature space relates uncorrelation and independence, allowing to analyze the second order statistics as it is encountered in traditional signal processing. As a result, the possibility of utilizing well known correlation tools arises, motivating the usage of Canonical Correlation Analysis as the main tool for detecting independence. Comparative simulation results are provided using a model based on fading AWGN channels.Peer ReviewedPostprint (published version

    Regularized estimation of information via canonical correlation analysis on a finite-dimensional feature space

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    This paper aims to estimate the information between two random phenomena by using consolidated second-order statistics tools. The squared-loss mutual information, a surrogate of the Shannon mutual information, is chosen due to its property of being expressed as a second-order moment. We first review the rationale for i.i.d. discrete sources, which involves mapping the data onto the simplex space, and we highlight the links with other well-known related concepts in the literature based on local approximations of information-theoretic measures. Then, the problem is translated to analog sources by mapping the data onto the characteristic space, focusing on the adaptability between the discrete and the analog case and its limitations. The proposed approach gains interpretability and scalability for its use on large data sets, providing a unified rationale for the free regularization parameters. Moreover, the structure of the proposed mapping allows resorting to Szegö’s theorem to reduce the complexity for high dimensional mappings, exhibiting a strong duality with spectral analysis. The performance of the developed estimators is analyzed using Gaussian mixtures.This work has been supported by the Spanish Ministry of Science and Innovation through project RODIN (PID2019-105717RB- C22/MCIN/AEI/10.13039/501100011033), by the grant 2021 SGR 01033 (AGAUR, Generalitat de Catalunya), and fellowship FI 2019 by the Secretary for University and Research of the Generalitat de Catalunya and the European Social Fund.Peer ReviewedPostprint (author's final draft

    On the estimation of Tsallis entropy and a novel information measure based on its properties

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    This letter explores a plug-in estimator of second-order Tsallis entropy based on Kernel Density Estimation (KDE) and its implicit regularization process. First, it is shown that the expected value of the estimator corresponds to the entropy of an Additive White Gaussian Noise (AWGN) model. Then, we prove various relevant properties of the Tsallis entropy: It is monotonically non-decreasing under random variables addition, its derivative with respect to the Gaussian noise power is monotonically non-increasing, and it is concave in the additive noise power. From these, we derive an information metric that provides an alternative to the strategy of regularization.This work was supported in part by the Spanish Ministry of Science and Innovation project RODIN under Grant PID2019-105717RB-C22, in part by Generalitat de Catalunya under Grant 2021 SGR 01033, in part by Fellowship 2019 FI 00620 and Fellowship 2023 FI “Joan Oró” 00050 by the Generalitat de Catalunya and the European Social Fund, and in part by Fellowship 2022 FPI-UPC 028 by the Universitat Politècnica de Catalunya and Banc de Santander. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Giuseppe Thadeu Freitas de AbreuPeer ReviewedPostprint (published version

    Robust estimation of the magnitude squared coherence based on Kernel signal processing

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    © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.A new outlier-robust approach to estimate the magnitude squared coherence of a random vector sequence, a common task required in a variety of estimation and detection problems, is proposed. The proposed estimator is based on Renyi's entropy, an information theoretic kernel-based measure that proves to be inversely proportional to the determinant of a regularized version of the covariance matrix in the proper Gaussian case. The trade-off between accuracy and robustness in terms of bias and variance is analytically and numerically characterized, showing a dependence on the relative kernel bandwidth and the available data size.Peer ReviewedPostprint (published version

    Entropy-based covariance determinant estimation

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    © 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.An information-theoretic approach is described to estimate the determinant of the covariance matrix of a random vector sequence (a common task in a wide range of estimation and detection problems in signal processing for communications). The method is based on a prior entropy-based processing of the data using kernels and offers robustness against small-entropy contamination. The trade-off between optimality, accuracy and robustness is analyzed, along with the impact of the relative kernel bandwidth and data size.Peer ReviewedPostprint (published version

    Multi-satellite cycle-slip detection and exclusion using the noise subspace of residual dynamics

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    Real-time detection of cycle-slips on undifferenced carrier-phase measurements is an important task to properly exclude wrong phase trackers from precise positioning algorithms. The detection is especially challenging in high-dynamic mobile scenarios, where traditional approaches (as those based on single-channel polynomial fitting) may easily lead to false positives. Using a multi-channel formulation of the problem, the proposed technique takes benefit of the available data redundancy (high number of tracked satellites) in order to ameliorate the false positives. This robustness is accomplished by adaptively estimating the orthogonal subspace spanned by the polynomial time-varying residuals obtained from all available channels (treated as a vector process), and using that subspace to form efficient channel combinations with cancelled satellite-receiver dynamics. The main advantage of the multi-channel approach is that wrong measurements can be discarded without needing any positioning estimate nor phase-ambiguity solver, thus improving the accuracy, reliability and integrity of positioning. The performance improvement is shown by means of theoretical analysis and computer simulations.Peer ReviewedPostprint (published version

    Sonda Rf para seguimiento no-invasivo de implantes médicos (stents)

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    Stents are medical devices that are implanted inside blood vessels to restore partial occlusions (stenosis). These devices (Fig. 1) are made of a frame of filaments (usually metallic) following a geometry that allows the frame to expand when a radial pressure is exerted. To implant them, stents are crimped around inflatable balloon catheters which are used to position the stent at the vessel occlusion. Once properly placed, the balloon is inflated and the stent is fixed to the vessel wall, restoring the appropriate vessel lumen. The balloon can be subsequently deflated an

    Sonda Rf para seguimiento no-invasivo de implantes médicos (stents)

    No full text
    Stents are medical devices that are implanted inside blood vessels to restore partial occlusions (stenosis). These devices (Fig. 1) are made of a frame of filaments (usually metallic) following a geometry that allows the frame to expand when a radial pressure is exerted. To implant them, stents are crimped around inflatable balloon catheters which are used to position the stent at the vessel occlusion. Once properly placed, the balloon is inflated and the stent is fixed to the vessel wall, restoring the appropriate vessel lumen. The balloon can be subsequently deflated an
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