Fourth Order Tensor

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Jurgen Finsterbusch - One of the best experts on this subject based on the ideXlab platform.

  • a Tensor model and measures of microscopic anisotropy for double wave vector diffusion weighting experiments with long mixing times
    Journal of Magnetic Resonance, 2010
    Co-Authors: Marco Lawrenz, Martin Koch, Jurgen Finsterbusch
    Abstract:

    Experiments with two diffusion-weighting periods applied successively in a single experiment, so-called double-wave-vector (DWV) diffusion-weighting experiments, are a promising tool for the investigation of material or tissue structure on a microscopic level, e.g. to determine cell or compartment sizes or to detect pore or cell anisotropy. However, the theoretical descriptions presented so far for experiments that aim to investigate the microscopic anisotropy with a long mixing time between the two diffusion weightings, are limited to certain wave vector orientations, specific pore shapes, and macroscopically isotropic samples. Here, the signal equations for fully restricted diffusion are re-investigated in more detail. A general description of the signal behavior for arbitrary wave vector directions, pore or cell shapes, and orientation distributions of the pores or cells is obtained that involves a Fourth-Order Tensor approach. From these equations, a rotationally invariant measure of the microscopic anisotropy, termed MA, is derived that yields information complementary to that of the (macroscopic) anisotropy measures of standard diffusion-Tensor acquisitions. Furthermore, the detailed angular modulation for arbitrary cell shapes with an isotropic orientation distribution is derived. Numerical simulations of the MR signal with a Monte-Carlo algorithms confirm the theoretical considerations. The extended theoretical description and the introduction of a reliable measure of the microscopic anisotropy may help to improve the applicability and reliability of corresponding experiments.

Dafalias Y. F. - One of the best experts on this subject based on the ideXlab platform.

  • Implicit integration of incrementally non-linear, zero- elastic range, bounding surface plasticity
    'Elsevier BV', 2019
    Co-Authors: Petalas Alexandros, Dafalias Y. F.
    Abstract:

    The zero elastic range, bounding surface plasticity framework is a suitable choice for modeling materials which exhibit zero purely elastic response during shearing. As a consequence of zero elastic range the plastic strain increment direction, and consequently the elastic-plastic moduli Fourth Order Tensor depends on the direction of the stress increment, rendering the model incrementally non-linear. The system of ordinary differential equations of the elastic-plastic formulation is intrinsically implicit. Thus, an iterative algorithm based on the Backward Euler numerical integration method and the damped Newton-Raphson method with an adaptive trial step is proposed in this work. The proposed methodology is applied to the zero elastic range SANISAND-Z model for sands and a thorough verification is done for various applied strain histories. The proposed integration scheme allows the use of SANISAND-Z or any other bounding surface zero elastic range model in displacement-driven finite element analysis

  • Numerical integration of the incrementally non-linear, zero elastic range, bounding surface plasticity model for sand
    CIMNE, 2017
    Co-Authors: Petalas A. L., Dafalias Y. F.
    Abstract:

    SANISAND-Z is a recently developed plasticity model for sands with zero purely elastic range in stress space within the framework of Bounding Surface (BS) plasticity. As a consequence of zero elastic range the plastic strain increment direction, and consequently the elastic-plastic moduli Fourth Order Tensor depends on the direction of the stress increment, rendering the model incrementally non-linear and intrinsically implicit. An iterative algorithm based on the Backward Euler method is presented to solve the non-linear system of ordinary differential equations. A non-traditional consistency condition based on the plastic multiplier is introduced as a core element of the system. A thorough analysis of the stability and accuracy of the algorithm is presented based on error estimation. The proposed integration scheme allows the use of SANISAND-Z framework in Finite Element Analysis

Michele Nazareth Da ,costa - One of the best experts on this subject based on the ideXlab platform.

  • Codificação Tensorial espaço-temporal para sistemas de comunicação sem fio MIMO
    2017
    Co-Authors: Michele Nazareth Da ,costa
    Abstract:

    Resumo: Desde o crescente sucesso de sistemas móveis na década de 90, novas tecnologias sem fio têm sido desenvolvidas a fim de suportar a crescente demanda de serviços de multimídia de alta qualidade e ainda flexível para implantar novos serviços com baixas taxas de erro. Uma forma interessante de melhorar o desempenho de erro e de obter melhores taxas de transmissão consiste em combinar o emprego de várias diversidades com técnicas de múltiplo acesso no contexto de sistemas MIMO. A incorporação de operações de sobreamostragem, espalhamento e multiplexação, e diversidades adicionais em sistemas sem fio levam a sinais recebidos multidimensionais que, naturalmente, satisfazem modelos Tensoriais. Esta tese propõe uma nova abordagem Tensorial baseada em uma codificação Tensorial espaço-temporal (TST) para sistemas de comunicação sem fio MIMO. Os sinais recebidos por múltiplas antenas formam um Tensor de quarta ordem que satisfaz um novo modelo Tensorial, referido como PARATUCK-(2,4). A análise de desempenho é realizada para o sistema proposto TST e um recente sistema espaço-tempo-frequencial (STF), a qual permite derivar expressões para o ganho máximo de diversidade através de um canal com desvanecimento plano. Propõe-se um sistema de transmissão baseado em codificação TST com recursos de alocação de antenas para sistemas MIMO com múltiplos usuários. Uma nova decomposição Tensorial é introduzida, denominada PARATUCK-(N1,N), e esta generaliza o modelo padrão PARATUCK-2 e nosso modelo PARATUCK-(2,4). A presente tese estabelece as condições de unicidade para o modelo PARATUCK-(N1,N). A partir desses resultados, a estimativa conjunta do símbolo e canal é assegurada para os sistemas TST e STF. Os receptores semi-cegos propostos para os dois sistemas baseiam-se no algoritmo do tipo mínimos quadrados alternados ("Alternanting Least Squares", ALS) e no método de otimização Levenberg-Marquardt (LM). Um receptor baseado na estrutura do produto de Kronecker, denominado "Kronecker Least Squares" (KLS), também é proposto para ambos os sistemas. Resultados de simulações são apresentados para ilustrar a eficiência dos receptores propostos em termos de recuperação de símbolo e a velocidade de convergência quando comparados com outros métodos da literatura.Abstract: Since the growing success of mobile systems in the 1990s, new wireless technologies have been developed in Order to support a growing demand for high-quality multimedia services while still being flexible to accommodate new services with low error rates. An interesting way to improve the error performance and to achieve better transmission rates is to combine the use of various diversities and multiplexing access techniques in the MIMO system context. The incorporation of oversampling, spreading and multiplexing operations and additional diversities on wireless systems lead to multidimensional received signals which naturally satisfy Tensor models. This thesis proposes a new Tensorial approach based on a Tensor space-time (TST) coding for MIMO wireless communication systems. The signals received by multiple antennas form a Fourth-Order Tensor that satisfies a new Tensor model, referred to as PARATUCK-(2,4) model. A performance analysis is carried out for the proposed TST system and a recent space-time-frequency (STF) system, which allows to derive expressions for the maximum diversity gain over a flat fading channel. An uplink processing based on the TST coding with allocation resources is proposed. A new Tensor decomposition is introduced, the so-called PARATUCK-(N1,N), which generalizes the standard PARATUCK-2 and our PARATUCK-(2,4) model. This thesis establishes uniqueness conditions for the PARATUCK-(N1,N) model. From these results, joint symbol and channel estimation is ensured for the TST and STF systems. Semi-blind receivers are proposed based on the well-known Alternating Least Squares (ALS) algorithm and the Levenberg-Marquardt (LM) method. A semi-blind receiver based on the Kronecker Least Squares (KLS) is also proposed for both systems. Simulation results are presented to illustrate the efficiency of the proposed receivers in terms of symbol recovery and convergence speed when compared to other methods from the literature

  • Tensor space-time coding for MIMO wireless communication systems
    2014
    Co-Authors: Michele Nazareth Da ,costa
    Abstract:

    Depuis le succès croissant des systèmes mobiles au cours des années 1990, les nouvelles technologies sans fil ont été développées afin de répondre à la demande croissante de services multimédias de haute qualité avec des taux d'erreur les plus faibles possibles. Un moyen intéressant pour améliorer les performances et obtenir de meilleurs taux de transmission consiste à combiner l'utilisation de plusieurs diversités avec un accès de multiplexage dans le cadre des systèmes MIMO. L'utilisation de techniques de sur-échantillonnage, d'étalement et de multiplexage, et de diversités supplémentaires conduit à des signaux multidimensionnels, au niveau de la réception, qui satisfont des modèles Tensoriels. Cette thèse propose une nouvelle approche Tensorielle basée sur un codage spatio-temporel Tensoriel (TST) pour les systèmes de communication sans fil MIMO. Les signaux reçus par plusieurs antennes forment un tenseur d'ordre quatre qui satisfait un nouveau modèle Tensoriel, modèle PARATUCK-(2,4) (PT-(2,4)). Une analyse de performance est réalisée pour le système TST ainsi que pour un système spatio-temporel-fréquentiel (STF) récemment proposé dans la littérature, avec l'obtention du gain maximum de diversité dans le cas d'un canal à évanouissement plat. Un système de transmission basé sur le codage TST est proposé pour les systèmes MIMO avec plusieurs utilisateurs. Une nouvelle décomposition Tensorielle est introduite, appelée PT-(N1,N). Cette thèse établit les conditions d'unicité du modèle PT-(N1,N). À partir de ces résultats, différents récepteurs semi-aveugles sont proposés pour une estimation conjointe des symboles transmis et du canal, pour les systèmes TST et STF.Since the growing success of mobile systems in the 1990s, new wireless technologies have been developed in Order to support a growing demand for high-quality multimedia services with low error rates. An interesting way to improve the error performance and to achieve better transmission rates is to combine the use of various diversities and multiplexing access techniques in the MIMO system context. The incorporation of oversampling, spreading and multiplexing operations and additional diversities on wireless systems lead to multidimensional received signals which naturally satisfy Tensor models. This thesis proposes a new Tensorial approach based on a Tensor space-time (TST) coding for MIMO wireless communication systems. The signals received by multiple antennas form a Fourth-Order Tensor that satisfies a new Tensor model, referred to as PARATUCK-(2,4) (PT-(2,4)) model. A performance analysis is carried out for the proposed TST system and a recent space-time-frequency (STF) system, which allows to derive expressions for the maximum diversity gain over a at fading channel. An uplink processing based on the TST coding with allocation resources is proposed. A new Tensor decomposition is introduced, the so-called PT-(N1,N), which generalizes the standard PT-2 and our PT-(2,4) model. This thesis establishes uniqueness conditions for the PARATUCK-(N1,N) model. From these results, joint symbol and channel estimation is ensured for the TST and STF systems. Semi-blind receivers are proposed based on the well-known Alternating Least Squares algorithm and the Levenberg-Marquardt method, and also a new receiver based on the Kronecker Least Squares (KLS) for both systems

  • Tensor space-time coding for MIMO wireless communication systems
    2014
    Co-Authors: Michele Nazareth Da ,costa, Favier Gérard, Travassos-romano, João Marcos, André De ,almeida
    Abstract:

    Depuis le succès croissant des systèmes mobiles au cours des années 1990, les nouvelles technologies sans fil ont été développées afin de répondre à la demande croissante de services multimédias de haute qualité avec des taux d'erreur les plus faibles possibles. Un moyen intéressant pour améliorer les performances et obtenir de meilleurs taux de transmission consiste à combiner l'utilisation de plusieurs diversités avec un accès de multiplexage dans le cadre des systèmes MIMO. L'utilisation de techniques de sur-échantillonnage, d'étalement et de multiplexage, et de diversités supplémentaires conduit à des signaux multidimensionnels, au niveau de la réception, qui satisfont des modèles Tensoriels. Cette thèse propose une nouvelle approche Tensorielle basée sur un codage spatio-temporel Tensoriel (TST) pour les systèmes de communication sans fil MIMO. Les signaux reçus par plusieurs antennes forment un tenseur d'ordre quatre qui satisfait un nouveau modèle Tensoriel, modèle PARATUCK-(2,4) (PT-(2,4)). Une analyse de performance est réalisée pour le système TST ainsi que pour un système spatio-temporel-fréquentiel (STF) récemment proposé dans la littérature, avec l'obtention du gain maximum de diversité dans le cas d'un canal à évanouissement plat. Un système de transmission basé sur le codage TST est proposé pour les systèmes MIMO avec plusieurs utilisateurs. Une nouvelle décomposition Tensorielle est introduite, appelée PT-(N1,N). Cette thèse établit les conditions d'unicité du modèle PT-(N1,N). À partir de ces résultats, différents récepteurs semi-aveugles sont proposés pour une estimation conjointe des symboles transmis et du canal, pour les systèmes TST et STF.Since the growing success of mobile systems in the 1990s, new wireless technologies have been developed in Order to support a growing demand for high-quality multimedia services with low error rates. An interesting way to improve the error performance and to achieve better transmission rates is to combine the use of various diversities and multiplexing access techniques in the MIMO system context. The incorporation of oversampling, spreading and multiplexing operations and additional diversities on wireless systems lead to multidimensional received signals which naturally satisfy Tensor models. This thesis proposes a new Tensorial approach based on a Tensor space-time (TST) coding for MIMO wireless communication systems. The signals received by multiple antennas form a Fourth-Order Tensor that satisfies a new Tensor model, referred to as PARATUCK-(2,4) (PT-(2,4)) model. A performance analysis is carried out for the proposed TST system and a recent space-time-frequency (STF) system, which allows to derive expressions for the maximum diversity gain over a at fading channel. An uplink processing based on the TST coding with allocation resources is proposed. A new Tensor decomposition is introduced, the so-called PT-(N1,N), which generalizes the standard PT-2 and our PT-(2,4) model. This thesis establishes uniqueness conditions for the PARATUCK-(N1,N) model. From these results, joint symbol and channel estimation is ensured for the TST and STF systems. Semi-blind receivers are proposed based on the well-known Alternating Least Squares algorithm and the Levenberg-Marquardt method, and also a new receiver based on the Kronecker Least Squares (KLS) for both systems.NICE-Bibliotheque electronique (060889901) / SudocSudocFranceF

  • Codificação Tensorial espaço-temporal para sistemas de comunicação sem fio MIMO
    Universidade Estadual de Campinas . Faculdade de Engenharia Elétrica e de Computação, 2014
    Co-Authors: Michele Nazareth Da ,costa
    Abstract:

    Desde o crescente sucesso de sistemas móveis na década de 90, novas tecnologias sem fio têm sido desenvolvidas a fim de suportar a crescente demanda de serviços de multimídia de alta qualidade e ainda flexível para implantar novos serviços com baixas taxas de erro. Uma forma interessante de melhorar o desempenho de erro e de obter melhores taxas de transmissão consiste em combinar o emprego de várias diversidades com técnicas de múltiplo acesso no contexto de sistemas MIMO. A incorporação de operações de sobreamostragem, espalhamento e multiplexação, e diversidades adicionais em sistemas sem fio levam a sinais recebidos multidimensionais que, naturalmente, satisfazem modelos Tensoriais. Esta tese propõe uma nova abordagem Tensorial baseada em uma codificação Tensorial espaço-temporal (TST) para sistemas de comunicação sem fio MIMO. Os sinais recebidos por múltiplas antenas formam um Tensor de quarta ordem que satisfaz um novo modelo Tensorial, referido como PARATUCK-(2,4). A análise de desempenho é realizada para o sistema proposto TST e um recente sistema espaço-tempo-frequencial (STF), a qual permite derivar expressões para o ganho máximo de diversidade através de um canal com desvanecimento plano. Propõe-se um sistema de transmissão baseado em codificação TST com recursos de alocação de antenas para sistemas MIMO com múltiplos usuários. Uma nova decomposição Tensorial é introduzida, denominada PARATUCK-(N1,N), e esta generaliza o modelo padrão PARATUCK-2 e nosso modelo PARATUCK-(2,4). A presente tese estabelece as condições de unicidade para o modelo PARATUCK-(N1,N). A partir desses resultados, a estimativa conjunta do símbolo e canal é assegurada para os sistemas TST e STF. Os receptores semi-cegos propostos para os dois sistemas baseiam-se no algoritmo do tipo mínimos quadrados alternados ("Alternanting Least Squares", ALS) e no método de otimização Levenberg-Marquardt (LM). Um receptor baseado na estrutura do produto de Kronecker, denominado "Kronecker Least Squares" (KLS), também é proposto para ambos os sistemas. Resultados de simulações são apresentados para ilustrar a eficiência dos receptores propostos em termos de recuperação de símbolo e a velocidade de convergência quando comparados com outros métodos da literatura.Since the growing success of mobile systems in the 1990s, new wireless technologies have been developed in Order to support a growing demand for high-quality multimedia services while still being flexible to accommodate new services with low error rates. An interesting way to improve the error performance and to achieve better transmission rates is to combine the use of various diversities and multiplexing access techniques in the MIMO system context. The incorporation of oversampling, spreading and multiplexing operations and additional diversities on wireless systems lead to multidimensional received signals which naturally satisfy Tensor models. This thesis proposes a new Tensorial approach based on a Tensor space-time (TST) coding for MIMO wireless communication systems. The signals received by multiple antennas form a Fourth-Order Tensor that satisfies a new Tensor model, referred to as PARATUCK-(2,4) model. A performance analysis is carried out for the proposed TST system and a recent space-time-frequency (STF) system, which allows to derive expressions for the maximum diversity gain over a flat fading channel. An uplink processing based on the TST coding with allocation resources is proposed. A new Tensor decomposition is introduced, the so-called PARATUCK-(N1,N), which generalizes the standard PARATUCK-2 and our PARATUCK-(2,4) model. This thesis establishes uniqueness conditions for the PARATUCK-(N1,N) model. From these results, joint symbol and channel estimation is ensured for the TST and STF systems. Semi-blind receivers are proposed based on the well-known Alternating Least Squares (ALS) algorithm and the Levenberg-Marquardt (LM) method. A semi-blind receiver based on the Kronecker Least Squares (KLS) is also proposed for both systems. Simulation results are presented to illustrate the efficiency of the proposed receivers in terms of symbol recovery and convergence speed when compared to other methods from the literature

André L. F. De Almeida - One of the best experts on this subject based on the ideXlab platform.

  • closed form channel estimation for mimo space time coded systems using a Fourth Order Tensor based receiver
    Circuits Systems and Signal Processing, 2018
    Co-Authors: Gilderlan T De Araujo, André L. F. De Almeida
    Abstract:

    In this short paper, a new Tensor-based receiver based on the Fourth-Order PARATUCK2 model combined with a structured PARAFAC model is formulated to solve the problem of channel estimation in a MIMO system. The proposed receiver is based on a modified space–time coding scheme that incorporates a formatting filter. Such a formatting filter is formed by a precoding matrix and a mapping matrix that load the coded signals to transmit antennas. The proposed receiver is divided into two steps. In the first step, closed-form channel estimation is performed by means of Kronecker and Khatri–Rao factorizations that rely on the singular value decomposition and the eigenvalue decomposition, respectively. In the second step, the transmitted symbols are linearly decoded from the estimated channel by exploiting the proposed space–time coding structure. Simulation results are presented to evaluate the performance of our Tensor-based receiver in terms of NMSE and BER, demonstrating an improved performance compared to competing schemes.

  • nested tucker Tensor decomposition with application to mimo relay systems using Tensor space time coding tstc
    Signal Processing, 2016
    Co-Authors: Gerard Favier, Alexandre C R Fernandes, André L. F. De Almeida
    Abstract:

    The aim of this paper is twofold. In a first part, we present a new Tensor decomposition that we call Tucker train decomposition or nested Tucker decomposition (NTD). NTD can be viewed as a particular case of Tensor-train decomposition recently proposed for representing and approximating high-dimensional Tensors in a compact way. NTD of a Fourth-Order Tensor is more specially analysed in terms of parameter estimation and uniqueness issue. In a second part, we show that the use of a Tensor space-time coding (TSTC) structure at both the source node and the relay node of a one-way two-hop multi-input multi-output (MIMO) relay communication system leads to a nested Tucker decomposition of the Fourth-Order Tensor formed by the signals received at the destination. Two semi-blind receivers are then proposed for jointly estimating the transmitted information symbols and the two individual relay channels. The first one is iterative, based on a three-step alternating least squares (ALS) algorithm, whereas the second one, denoted 2LSKP, is a closed-form solution based on the LS estimations of two Kronecker products. Two supervised receivers are also derived by using a (short) pilot-assisted closed-form solution for calculating channel estimates. These estimates are exploited either for initializing the ALS receiver or for designing a zero-forcing (ZF) receiver. Extensive Monte Carlo simulation results are provided to demonstrate the performance of the proposed relay system. HighlightsWe present a new Tensor model called a Tucker train decomposition or a nested Tucker decomposition (NTD).Assuming that the core Tensors are known, we propose two algorithms for estimating the matrix factors of a NTD(4).We show that a NTD(4) allows to model a one-way two-hop MIMO relay system with TSTC at the source and the relay.We derive two semi-blind receivers allowing to jointly estimate the information symbols and the two individual relay channels.We demonstrate the effectiveness of the proposed receivers by means of Monte Carlo simulations.

  • Fourth-Order Tensor method for blind spatial signature estimation
    2014 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2014
    Co-Authors: Paulo R. B. Gomes, André L. F. De Almeida, Joao Paulo C. L. Da Costal
    Abstract:

    In this paper, we consider a wireless communication scenario where M sources simultaneously transmit towards a base station equipped with an array of K sensors. A new method is proposed to solve the spatial signature estimation problem without resorting to training sequences and without knowledge of sources' covariance structure. By assuming that the sources' amplitudes vary between successive time blocks, a Fourth-Order Tensor decomposition of the multimode spatio-temporal data covariance is proposed, from which an iterative algorithm is formulated to estimate sources' spatial signatures. A distinguishing feature of the proposed Tensor method is its efficiency in treating the case where the sources' covariance matrix is non-diagonal and unknown, which generally happens when working with sample data covariances computed from a reduced number of snapshots.

Sabine Heiland - One of the best experts on this subject based on the ideXlab platform.

  • fiber tracking of human brain using Fourth Order Tensor and high angular resolution diffusion imaging
    Magnetic Resonance in Medicine, 2008
    Co-Authors: M R Jayachandra, N Rehbein, Christian Herweh, Sabine Heiland
    Abstract:

    The accuracy of fiber tracking on the basis of diffusion Tensor magnetic resonance imaging (DTI) is affected by many parameters. To increase accuracy of the tracking algorithm, we introduce DTI with a Fourth-Order Tensor. Tensor elements comprise information obtained by high angular resolution diffusion imaging (HARDI). We further developed the flattened high rank Tensor (FLAHRT) method and applied it to the measured Fourth-Order Tensor. We then compared FLAHRT with: 1) the standard tracking algorithm using a second-Order Tensor; and 2) existing techniques involving the representation of conventional second-Order Tensor components as a weighted average of Fourth-Order Tensor elements. Such techniques have been formulated in recent DT studies to link high-rank to low-rank Cartesian diffusion Tensors (DTs). Diagonalization of the second-Order Tensor decomposes the Tensor into three eigenvalues and three eigenvectors, which in turn are used to describe the diffusivity profile of a particular voxel. Diagonalization after application of the FLAHRT method reveals six eigenvalues and six eigenTensors, resulting in a more accurate description of the anisotropy. We performed fiber tracking based on the eigenvalues and eigenTensors calculated with the FLAHRT and standard methods. We could show that the FLAHRT technique gives more consistent and more accurate results even with a data set acquired in 15 directions only. The decomposition of the Fourth-Order Tensor into six eigenTensors has the potential to describe six different fiber orientations within a voxel.