The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform

Eric Moreau - One of the best experts on this subject based on the ideXlab platform.

  • a two step algorithm for joint eigenvalue decomposition application to canonical polyadic decomposition of fluorescence spectra
    Chemometrics and Intelligent Laboratory Systems, 2020
    Co-Authors: Remi Andre, Xavier Luciani, Laurent Albera, Eric Moreau
    Abstract:

    Abstract In this paper, we propose a new Joint EigenValue Decomposition (JEVD) algorithm. JEVD problem belongs to the family of joint diagonalization problems. Hence, JEVD algorithms aim at estimating the common basis of eigenvectors of a matrix set. This problem occurs in many signal processing applications. It has notably allowed to develop efficient algorithms for the Canonical Polyadic Decomposition (CPD) of multiway arrays. The proposed JEVD algorithm is based on an original two-step approach. The first step consists in transforming the considered matrix set into a set of positive definite matrices. In this purpose, we introduce an ad hoc joint symmetrization algorithm. This first step allows us to transform the JEVD problem into a simpler orthogonal joint diagonalization problem. The second step is then performed using an efficient orthogonal joint diagonalization algorithm of the literature. Eventually, the performance of the proposed approach is deeply investigated in the CPD context of multidimensional fluorescence data. More particularly, we consider difficult scenarios such as the cases of an overestimated rank and highly correlated factors.

  • nonorthogonal joint diagonalization zero diagonalization for source separation based on time frequency distributions
    IEEE Transactions on Signal Processing, 2007
    Co-Authors: E M Fadaili, N T Moreau, Eric Moreau
    Abstract:

    This paper deals with the blind separation of instantaneous mixtures of source signals using time-frequency distributions (TFDs). We propose iterative algorithms to perform the nonorthogonal zero diagonalization and/or joint diagonalization of given sets of matrices. As an application, we show that the source separation can be realized by applying one of these algorithms to a set of spatial quadratic TFD matrices corresponding only to the so-called cross-source terms and/or to the so-called autosource terms. The determination of the above matrices to be jointly decomposed requires first an automatic selection procedure of useful time-frequency points. Regarding this last point, we also propose a new selection procedure and a modification of an existing one and provide a comparison with other existing ones. The nonorthogonal joint diagonalization and/or zero diagonalization algorithm's main advantage is to not require (in the blind source separation context) a prewhitening stage, which allows them to work even with a class of correlated signals and provides generally improved separation performance. Finally, an analytical example and computer simulations are provided in order to illustrate the effectiveness of the proposed approach and to compare it with classical ones

  • algorithme de zero Diagonalisation conjointe pour la separation de sources deterministes
    20° Colloque sur le traitement du signal et des images 2005 ; p. 795-798, 2005
    Co-Authors: E M Fadaili, Nadege Thirionmoreau, Eric Moreau
    Abstract:

    The problem of blind separation of deterministic sources based on joint zero-diagonalization of a particular set of spatial quadratic time-frequency matrices is considered. We propose a new non unitary joint zero-diagonalization algorithm. It is obtained thanks to the parametric optimization of a criterium we give. The advantage of such an approach is that it does not require a pre-whitening stage any more. We also detail a time-frequency points selection procedure used in order to build the set of matrices to be joint zero-diagonalized. Finally, computer simulations illustrate the effectiveness of the proposed algorithm by comparing it with other ones based on unitary or non unitary joint-diagonalization and on unitary joint zero-diagonalization.

  • a generalization of joint diagonalization criteria for source separation
    IEEE Transactions on Signal Processing, 2001
    Co-Authors: Eric Moreau
    Abstract:

    In the field of blind source separation, joint-diagonalization-based approaches constitute an important framework, leading to useful algorithms such as the popular joint approximate diagonalization of eigenmatrices (JADE) and simultaneous third-order tensor diagonalization (STOTD) algorithms. However, they are often restricted to the case of cumulants of order four. In this paper, we extend the results leading to JADE and STOTD to cumulants of any order greater than or equal to three by exhibiting a new family of contrast functions that constitutes then a unified framework for the above known results. This also leads us to generalize some links between contrast functions and joint-diagonalization criteria on which these algorithms are based. In turn, one contrast of the new family allows us to show that a function previously proposed as a separation criterion is also a contrast. Moreover, for the two generalized JADE and STOTD contrasts, the analytical optimal solution in the case of two sources is derived and shown to keep the same simple expression, whatever the cumulant order. Finally, some computer simulations illustrate the potential advantage one can take by considering statistics of different orders for the joint-diagonalization of cumulant matrices.

John G Mcwhirter - One of the best experts on this subject based on the ideXlab platform.

  • sequential matrix diagonalization algorithms for polynomial evd of parahermitian matrices
    IEEE Transactions on Signal Processing, 2015
    Co-Authors: Soydan Redif, Stephan Weiss, John G Mcwhirter
    Abstract:

    For parahermitian polynomial matrices, which can be used, for example, to characterize space-time covariance in broadband array processing, the conventional eigenvalue decomposition (EVD) can be generalized to a polynomial matrix EVD (PEVD). In this paper, a new iterative PEVD algorithm based on sequential matrix diagonalization (SMD) is introduced. At every step the SMD algorithm shifts the dominant column or row of the polynomial matrix to the zero lag position and eliminates the resulting instantaneous correlation. A proof of convergence is provided, and it is demonstrated that SMD establishes diagonalization faster and with lower order operations than existing PEVD algorithms.

  • reduced search space multiple shift maximum element sequential matrix Diagonalisation algorithm
    2nd IET International Conference on Intelligent Signal Processing 2015 (ISP), 2015
    Co-Authors: Jamie Corr, Keith Thompson, Ian K. Proudler, Stephan Weiss, John G Mcwhirter
    Abstract:

    The Multiple Shift Maximum Element Sequential Matrix Diagonalisation (MSME-SMD) algorithm is a powerful but costly method for performing approximate polynomial eigenvalue decomposition (PEVD) for space-time covariance-type matrices encountered in e.g. broadband array processing. This paper discusses a newly developed search method that restricts the order growth within the MSME-SMD algorithm. In addition to enhanced control of the polynomial degree of the paraunitary and parahermitian factors in this decomposition, the new search method is also computationally less demanding as fewer elements are searched compared to the original while the excellent Diagonalisation of MSME-SMD is maintained.

  • causality constrained multiple shift sequential matrix Diagonalisation for parahermitian matrices
    European Signal Processing Conference, 2014
    Co-Authors: Jamie Corr, Keith Thompson, Stephan Weiss, John G Mcwhirter, Ian K. Proudler
    Abstract:

    This paper introduces a causality constrained sequential matrix Diagonalisation (SMD) algorithm, which generates a causal paraunitary transformation that aprroximately diagonalises and spectrally majorises a parahermitian matrix, and can be used to determine a polynomial eigenvalue decomposition. This algorithm builds on a multiple shift technique which speeds up Diagonalisation by Diagonalisation per iteration step based on a particular search space, which is contrained to permit a maximum number of causal time shifts. The results presented in this paper show the performance in comparison to existing algorithms, in particular an unconstrained multiple shift SMD algorithm, from which our proposed method derives.

Ian K. Proudler - One of the best experts on this subject based on the ideXlab platform.

  • Divide-and-Conquer Sequential Matrix Diagonalisation for Parahermitian Matrices
    2017 Sensor Signal Processing for Defence Conference (SSPD), 2017
    Co-Authors: Fraser K. Coutts, Jamie Corr, Keith Thompson, Ian K. Proudler, Stephan Weiss
    Abstract:

    A number of algorithms capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is a generalisation of the ordinary EVD and will diagonalise a parahermitian matrix via paraunitary operations. Inspired by the existence of low complexity divide-and-conquer solutions to eigenproblems, this paper addresses a divide-and-conquer approach to the PEVD utilising the sequential matrix Diagonalisation (SMD) algorithm. We demonstrate that with the proposed techniques, encapsulated in a novel algorithm titled divide-and-conquer sequential matrix Diagonalisation (DC-SMD), algorithm complexity can be significantly reduced. This reduction impacts on a number of broadband multichannel problems, including those involving large arrays.

  • reduced search space multiple shift maximum element sequential matrix Diagonalisation algorithm
    2nd IET International Conference on Intelligent Signal Processing 2015 (ISP), 2015
    Co-Authors: Jamie Corr, Keith Thompson, Ian K. Proudler, Stephan Weiss, John G Mcwhirter
    Abstract:

    The Multiple Shift Maximum Element Sequential Matrix Diagonalisation (MSME-SMD) algorithm is a powerful but costly method for performing approximate polynomial eigenvalue decomposition (PEVD) for space-time covariance-type matrices encountered in e.g. broadband array processing. This paper discusses a newly developed search method that restricts the order growth within the MSME-SMD algorithm. In addition to enhanced control of the polynomial degree of the paraunitary and parahermitian factors in this decomposition, the new search method is also computationally less demanding as fewer elements are searched compared to the original while the excellent Diagonalisation of MSME-SMD is maintained.

  • causality constrained multiple shift sequential matrix Diagonalisation for parahermitian matrices
    European Signal Processing Conference, 2014
    Co-Authors: Jamie Corr, Keith Thompson, Stephan Weiss, John G Mcwhirter, Ian K. Proudler
    Abstract:

    This paper introduces a causality constrained sequential matrix Diagonalisation (SMD) algorithm, which generates a causal paraunitary transformation that aprroximately diagonalises and spectrally majorises a parahermitian matrix, and can be used to determine a polynomial eigenvalue decomposition. This algorithm builds on a multiple shift technique which speeds up Diagonalisation by Diagonalisation per iteration step based on a particular search space, which is contrained to permit a maximum number of causal time shifts. The results presented in this paper show the performance in comparison to existing algorithms, in particular an unconstrained multiple shift SMD algorithm, from which our proposed method derives.

Stephan Weiss - One of the best experts on this subject based on the ideXlab platform.

  • Divide-and-Conquer Sequential Matrix Diagonalisation for Parahermitian Matrices
    2017 Sensor Signal Processing for Defence Conference (SSPD), 2017
    Co-Authors: Fraser K. Coutts, Jamie Corr, Keith Thompson, Ian K. Proudler, Stephan Weiss
    Abstract:

    A number of algorithms capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is a generalisation of the ordinary EVD and will diagonalise a parahermitian matrix via paraunitary operations. Inspired by the existence of low complexity divide-and-conquer solutions to eigenproblems, this paper addresses a divide-and-conquer approach to the PEVD utilising the sequential matrix Diagonalisation (SMD) algorithm. We demonstrate that with the proposed techniques, encapsulated in a novel algorithm titled divide-and-conquer sequential matrix Diagonalisation (DC-SMD), algorithm complexity can be significantly reduced. This reduction impacts on a number of broadband multichannel problems, including those involving large arrays.

  • reduced search space multiple shift maximum element sequential matrix Diagonalisation algorithm
    2nd IET International Conference on Intelligent Signal Processing 2015 (ISP), 2015
    Co-Authors: Jamie Corr, Keith Thompson, Ian K. Proudler, Stephan Weiss, John G Mcwhirter
    Abstract:

    The Multiple Shift Maximum Element Sequential Matrix Diagonalisation (MSME-SMD) algorithm is a powerful but costly method for performing approximate polynomial eigenvalue decomposition (PEVD) for space-time covariance-type matrices encountered in e.g. broadband array processing. This paper discusses a newly developed search method that restricts the order growth within the MSME-SMD algorithm. In addition to enhanced control of the polynomial degree of the paraunitary and parahermitian factors in this decomposition, the new search method is also computationally less demanding as fewer elements are searched compared to the original while the excellent Diagonalisation of MSME-SMD is maintained.

  • sequential matrix diagonalization algorithms for polynomial evd of parahermitian matrices
    IEEE Transactions on Signal Processing, 2015
    Co-Authors: Soydan Redif, Stephan Weiss, John G Mcwhirter
    Abstract:

    For parahermitian polynomial matrices, which can be used, for example, to characterize space-time covariance in broadband array processing, the conventional eigenvalue decomposition (EVD) can be generalized to a polynomial matrix EVD (PEVD). In this paper, a new iterative PEVD algorithm based on sequential matrix diagonalization (SMD) is introduced. At every step the SMD algorithm shifts the dominant column or row of the polynomial matrix to the zero lag position and eliminates the resulting instantaneous correlation. A proof of convergence is provided, and it is demonstrated that SMD establishes diagonalization faster and with lower order operations than existing PEVD algorithms.

  • causality constrained multiple shift sequential matrix Diagonalisation for parahermitian matrices
    European Signal Processing Conference, 2014
    Co-Authors: Jamie Corr, Keith Thompson, Stephan Weiss, John G Mcwhirter, Ian K. Proudler
    Abstract:

    This paper introduces a causality constrained sequential matrix Diagonalisation (SMD) algorithm, which generates a causal paraunitary transformation that aprroximately diagonalises and spectrally majorises a parahermitian matrix, and can be used to determine a polynomial eigenvalue decomposition. This algorithm builds on a multiple shift technique which speeds up Diagonalisation by Diagonalisation per iteration step based on a particular search space, which is contrained to permit a maximum number of causal time shifts. The results presented in this paper show the performance in comparison to existing algorithms, in particular an unconstrained multiple shift SMD algorithm, from which our proposed method derives.

Kazunobu Kondo - One of the best experts on this subject based on the ideXlab platform.

  • regularized fast multichannel nonnegative matrix factorization with ilrma based prior distribution of joint diagonalization process
    International Conference on Acoustics Speech and Signal Processing, 2020
    Co-Authors: Keigo Kamo, Yuki Kubo, Norihiro Takamune, Daichi Kitamura, Hiroshi Saruwatari, Yu Takahashi, Kazunobu Kondo
    Abstract:

    In this paper, we address a convolutive blind source separation (BSS) problem and propose a new extended framework of FastMNMF by introducing prior information for joint diagonalization of the spatial covariance matrix model. Recently, FastMNMF has been proposed as a fast version of multichannel nonnegative matrix factorization under the assumption that the spatial covariance matrices of multiple sources can be jointly diagonalized. However, its source-separation performance was not improved and the physical meaning of the joint-diagonalization process was unclear. To resolve these problems, we first reveal a close relationship between the joint-diagonalization process and the demixing system used in independent low-rank matrix analysis (ILRMA). Next, motivated by this fact, we propose a new regularized FastMNMF supported by ILRMA and derive convergence-guaranteed parameter update rules. From BSS experiments, we show that the proposed method outperforms the conventional FastMNMF in source-separation accuracy with almost the same computation time.