Nuestros investigadores

Jesús Gutiérrez Gutiérrez

Departamento
Departamento de Ingeniería Biomédica y Ciencias
Escuela de Ingenieros (TECNUN). Universidad de Navarra
Líneas de investigación
Análisis matricial; Teoría de la información, Procesado estadístico de señales

Publicaciones científicas más recientes (desde 2010)

Autores: Zárraga-Rodríguez, M.; Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia); Insausti, Xabier;
Revista: ENTROPY
ISSN 1099-4300  Vol. 21  Nº 10  2019  págs. 965
In this paper, we present a low-complexity coding strategy to encode (compress) finite-length data blocks of Gaussian vector sources. We show that for large enough data blocks of a Gaussian asymptotically wide sense stationary (AWSS) vector source, the rate of the coding strategy tends to the lowest possible rate. Besides being a low-complexity strategy it does not require the knowledge of the correlation matrix of such data blocks. We also show that this coding strategy is appropriate to encode the most relevant Gaussian vector sources, namely, wide sense stationary (WSS), moving average (MA), autoregressive (AR), and ARMA vector sources.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia); Villar-Rosety, F. M.; Zárraga-Rodríguez, M.; et al.
Revista: IEEE COMMUNICATIONS LETTERS
ISSN 1089-7798  Vol. 23  Nº 5  2019  págs. 773 - 776
In this letter, we give a low-complexity analog linear coding scheme for transmitting finite-length data blocks of asymptotically wide sense stationary (AWSS) autoregressive (AR) sources through additive white Gaussian noise (AWGN) channels.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia)
Revista: APPLIED MATHEMATICS AND COMPUTATION
ISSN 0096-3003  Vol. 362  Nº 124526  2019 
The Pisarenko method estimates the power spectral density (PSD) of Gaussian wide sense stationary (WSS) 1-dimensional (scalar) processes when the PSD is Lipschitz. In this paper we modify the Pisarenko method to estimate the generating function of a sequence of block Toeplitz matrices from another sequence of matrices when both sequences are asymptotically equivalent. This modified version of the Pisarenko method allows us to estimate the PSD of any asymptotically WSS (AWSS) multidimensional (vector) process even if the process is not Gaussian and even if the PSD is continuous, but not Lipschitz.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia); Zárraga-Rodríguez, M.; Villar-Rosety, F. M.; et al.
Revista: ENTROPY
ISSN 1099-4300  Vol. 20  Nº 6  2018 
In this paper, we give upper bounds for the rate-distortion function (RDF) of any Gaussian vector, and we propose coding strategies to achieve such bounds. We use these strategies to reduce the computational complexity of coding Gaussian asymptotically wide sense stationary (AWSS) autoregressive (AR) sources. Furthermore, we also give sufficient conditions for AR processes to be AWSS.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia); Zárraga-Rodríguez, M.; Insausti, Xabier;
Revista: SENSORS
ISSN 1424-8220  Vol. 18  Nº 4  2018 
In this paper, we compare six known linear distributed average consensus algorithms on a sensor network in terms of convergence time (and therefore, in terms of the number of transmissions required). The selected network topologies for the analysis (comparison) are the cycle and the path. Specifically, in the present paper, we compute closed-form expressions for the convergence time of four known deterministic algorithms and closed-form bounds for the convergence time of two known randomized algorithms on cycles and paths. Moreover, we also compute a closed-form expression for the convergence time of the fastest deterministic algorithm considered on grids.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia); Zárraga-Rodríguez, M.; Crespo, Pedro M.; et al.
Revista: ENTROPY
ISSN 1099-4300  Vol. 20  Nº 9  2018  págs. 719
Autores: Insausti, Xabier; Crespo, Pedro M.; Gutiérrez-Gutiérrez, Jesús; et al.
Revista: IEEE COMMUNICATIONS LETTERS
ISSN 1089-7798  Vol. 22  Nº 9  2018  págs. 1754 - 1757
In this letter, we design a low-latency, low-complexity, and low-transmission power analog linear coding scheme to estimate the finite-length data blocks under a mean-square-error (distortion) criterion. The proposed scheme is based on the analog linear coding and the discrete Fourier transform. A remarkable feature of our scheme is that it does not require knowing the correlation matrix of the data blocks, and therefore, it can be used even if the correlation matrix changes slowly with time.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia); Zárraga-Rodríguez, M.; Insausti, Xabier;
Revista: ENTROPY
ISSN 1099-4300  Vol. 19  Nº 554  2017 
In this paper, we present upper bounds for the rate distortion function (RDF) of finite-length data blocks of Gaussian wide sense stationary (WSS) sources and we propose coding strategies to achieve such bounds. In order to obtain those bounds, we previously derive new results on the discrete Fourier transform (DFT) of WSS processes.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia); Zárraga-Rodríguez, M.; Insausti, Xabier; et al.
Revista: ENTROPY
ISSN 1099-4300  Vol. 19  Nº 95  2017 
In the present paper, we obtain a result on the rate-distortion function (RDF) of wide sense stationary (WSS) vector processes that allows us to reduce the complexity of coding those processes. To achieve this result, we propose a sequence of block circulant matrices. In addition, we use the proposed sequence to reduce the complexity of filtering WSS vector processes.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia); Crespo, Pedro M.; Zárraga-Rodríguez, M.; et al.
Revista: IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN 0018-9448  Vol. 63  Nº 9  2017  págs. 6000 - 6003
Using some recent results on asymptotically equivalent sequences of matrices, we present in this paper, a new derivation of the capacity formula given by Brandenburg and Wyner for a discrete-time Gaussian multiple-input-multiple-output channel with memory. In this paper, we tackle not only the case considered by them, where the number of channel inputs and the number of channel outputs are the same, but also when both numbers are different.
Autores: Insausti, Xabier, (Autor de correspondencia); Gutiérrez-Gutiérrez, Jesús; Zárraga-Rodríguez, M.; et al.
Revista: SENSORS
ISSN 1424-8220  Vol. 17  Nº 1702  2017 
In a network, a distributed consensus algorithm is fully characterized by its weighting matrix. Although there exist numerical methods for obtaining the optimal weighting matrix, we have not found an in-network implementation of any of these methods that works for all network topologies. In this paper, we propose an in-network algorithm for finding such an optimal weighting matrix.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia); Zárraga-Rodríguez, M.;
Revista: APPLIED MATHEMATICS AND COMPUTATION
ISSN 0096-3003  Vol. 289  2016  págs. 214 - 219
In this paper we present a singular value decomposition for any n x n + 1 complex upper bidiagonal Toeplitz matrix.
Autores: Gutiérrez-Gutiérrez, Jesús; Zárraga-Rodríguez, M.;
Revista: SPECIAL MATRICES
ISSN 2300-7451  Vol. 4  Nº 1  2016  págs. 73-79
In this paper, we obtain an eigenvalue decomposition for any complex skew-persymmetric anti-tridiagonal Hankel matrix where the eigenvector matrix is orthogonal.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia)
Revista: APPLIED MATHEMATICS AND COMPUTATION
ISSN 0096-3003  Vol. 234  2014  págs. 333 - 338
In this paper, we present an eigenvalue decomposition for any complex persymmetric Hankel matrix with at most three non-zero anti-diagonals. Furthermore, we derive a general expression for the natural powers of these Hankel matrices in terms of the natural powers of complex persymmetric anti-tridiagonal Hankel matrices.
Autores: Insausti, Xabier; Camaro, F.; Crespo, Pedro M.; et al.
Revista: IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING
ISSN 1932-4553  Vol. 7  Nº 2  2013  págs. 163 - 174
In this paper, we design a practical power-efficient algorithm for Wireless Sensor Networks (WSN) in order to obtain, in a distributed manner, the projection of an observed sampled spatial field on a subspace of lower dimension. This is an important problem that is motivated in various applications where there are well defined subspaces of interest (e. g., spectral maps in cognitive radios). As opposed to traditional Gossip Algorithms used for subspace projection, where separation of channel coding and computation is assumed, our algorithm combines binary finite-length Computational Coding and a novel gossip-like protocol with certain communication rules, achieving important savings in convergence time and yielding a decrease in energy consumption as the density of the network increases, as compared to a separation scheme.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia)
Revista: APPLIED MATHEMATICS AND COMPUTATION
ISSN 0096-3003  Vol. 222  2013  págs. 472 - 477
In this paper, we present an eigenvalue decomposition for any n x n complex matrix with constant diagonals T-n = (a(j-k))(j,k-1)(n) satisfying that there exists a positive integer m such that a(k) = 0 for all k is not an element of {-m, 0, m}. Moreover, from this eigenvalue decomposition we obtain a singular value decomposition for any comb filter matrix.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia)
Revista: APPLIED MATHEMATICS AND COMPUTATION
ISSN 0096-3003  Vol. 219  Nº 17  2013  págs. 9219 - 9222
In this paper, we derive a general expression for the entries of the qth power (q is an element of N) of the n x n complex tridiagonal matrix tridiag(n)(a(1), a(0), a(-1)) for all n >= 2 (q - 1), in terms of binomial coefficients. (C) 2013 Elsevier Inc. All rights reserved.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia)
Revista: LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN 0024-3795  Vol. 439  Nº 1  2013  págs. 34 - 54
In this paper we present an eigenvalue decomposition for any real symmetric tridiagonal 2-Toeplitz matrix of odd order, where the eigenvector matrix is orthogonal. Using this decomposition we study the entries of continuous functions of large real symmetric tridiagonal 2-Toeplitz matrices. Furthermore, we also study in the present paper the entries of continuous functions of large Hermitian Toeplitz matrices with at most three non-zero diagonals.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia); Crespo, Pedro M.;
Revista: IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN 0018-9448  Vol. 57  Nº 8  2011  págs. 5444 - 5454
The present paper considers a special class of vector random processes that we call multivariate asymptotically wide sense stationary (WSS) processes. A multivariate random process is said to be asymptotically WSS if it has constant mean and the sequence of its autocorrelation matrices is asymptotically equivalent (a. e.) to the sequence of autocorrelation matrices of some multivariate WSS process. It is shown that this class of processes contains meaningful processes other than multivariate WSS processes. In particular, we give sufficient conditions for multivariate moving average (MA) processes, multivariate autoregressive (AR) processes and multivariate autoregressive moving average (ARMA) processes to be asymptotically WSS. Furthermore, in order to solve multiple-input-multiple-output (MIMO) problems in communications and signal processing involving this kind of processes, we extend the Gray definition of a. e. sequences of matrices and his main results on these sequences to non-square matrices. As an example, the derived results on a. e. sequences of non-square matrices are applied to compute the differential entropy rate and the minimum mean square error (MMSE) for a linear predictor of a multivariate asymptotically WSS process.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia); Iglesias, I.; Podhorski, Adam;
Revista: SIGNAL PROCESSING
ISSN 0165-1684  Vol. 91  Nº 9  2011  págs. 2237 - 2245
In the present paper we derive a formula for the geometric minimum mean square error (GMMSE) for one-sided and two-sided finite-length vector linear predictors. This formula is written only in terms of the autocorrelation matrix of the vector process being predicted. We also obtain a formula for the GMMSE for one-sided and two-sided infinite-length vector linear predictors of any wide sense stationary (WSS) vector process. This GMMSE expression for the infinite-length case is derived from the GMMSE expression obtained for the finite-length case.
Autores: Gutiérrez-Gutiérrez, Jesús, (Autor de correspondencia)
Revista: APPLIED MATHEMATICS AND COMPUTATION
ISSN 0096-3003  Vol. 217  Nº 13  2011  págs. 6125 - 6132
In this paper, we derive a general expression for the entries of the powers of any complex persymmetric or skew-persymmetric anti-tridiagonal matrix with constant anti-diagonals, in terms of the Chebyshev polynomials of the second kind.

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  OTROS MÉRITOS RELEVANTES

Jesús Gutiérrez Gutiérrez es Licenciado en Matemáticas (especialidad de Matemática Fundamental) por la Universidad de Granada (1999) y Doctor por la Universidad de Navarra dentro del programa de doctorado de Electrónica y Comunicaciones (2004).
De octubre de 2004 a marzo de 2017 ha sido Investigador del Centro Tecnológico CEIT. Desde abril 2017 es Profesor Titular en el área de Matemática Aplicada en la Escuela de Ingenieros de la Universidad de Navarra (Tecnun). Desde Mayo de 2017 es Director del Departamento de Ingeniería Biomédica y Ciencias de Tecnun.