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Nicolas Dobigeon - One of the best experts on this subject based on the ideXlab platform.

  • Bayesian separation of spectral sources under non-negativity and full additivity constraints
    Signal Processing, 2009
    Co-Authors: Nicolas Dobigeon, Said Moussaoui, Jean-yves Tourneret
    Abstract:

    This paper addresses the problem of separating spectral sources which are linearly mixed with unknown proportions. The main difficulty of the problem is to ensure the full additivity (sum-to-one) of the mixing coefficients and non-negativity of sources and mixing coefficients. A Bayesian estimation approach based on Gamma priors was recently proposed to handle the non-negativity constraints in a linear mixture Model. However, incorporating the full additivity constraint requires further developments. This paper studies a new Hierarchical Bayesian Model appropriate to the non-negativity and sum-to-one constraints associated to the sources and the mixing coefficients of linear mixtures. The estimation of the unknown parameters of this Model is performed using samples obtained with an appropriate Gibbs algorithm. The performance of the proposed algorithm is evaluated through simulation results conducted on synthetic mixture data. The proposed approach is also applied to the processing of multicomponent chemical mixtures resulting from Raman spectroscopy.

  • Joint Bayesian Endmember Extraction and Linear Unmixing for Hyperspectral Imagery
    IEEE Transactions on Signal Processing, 2009
    Co-Authors: Nicolas Dobigeon, Jean-yves Tourneret, Said Moussaoui, Martial Coulon, Alfred O. Hero
    Abstract:

    This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing Model. The estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a Hierarchical Bayesian Model. This Model assumes conjugate prior distributions for these parameters, accounts for nonnegativity and full-additivity constraints, and exploits the fact that the endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution. This sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples. The accuracy of the joint Bayesian estimator is illustrated by simulations conducted on synthetic and real AVIRIS images.

  • Semi-Supervised Linear Spectral Unmixing Using a Hierarchical Bayesian Model for Hyperspectral Imagery
    IEEE Transactions on Signal Processing, 2008
    Co-Authors: Nicolas Dobigeon, Jean-yves Tourneret, Chein-i Chang
    Abstract:

    This paper proposes a Hierarchical Bayesian Model that can be used for semi-supervised hyperspectral image unmixing. The Model assumes that the pixel reflectances result from linear combinations of pure component spectra contaminated by an additive Gaussian noise. The abundance parameters appearing in this Model satisfy positivity and additivity constraints. These constraints are naturally expressed in a Bayesian context by using appropriate abundance prior distributions. The posterior distributions of the unknown Model parameters are then derived. A Gibbs sampler allows one to draw samples distributed according to the posteriors of interest and to estimate the unknown abundances. An extension of the algorithm is finally studied for mixtures with unknown numbers of spectral components belonging to a know library. The performance of the different unmixing strategies is evaluated via simulations conducted on synthetic and real data.

  • Blind unmixing of linear mixtures using a Hierarchical Bayesian Model. Application to spectroscopic signal analysis
    2007
    Co-Authors: Nicolas Dobigeon, Jean-yves Tourneret, Said Moussaoui
    Abstract:

    This paper addresses the problem of spectral unmixing when positivity and additivity constraints are imposed on the mixing coefficients. A Hierarchical Bayesian Model is introduced to satisfy these two constraints. A Gibbs sampler is then proposed to generate samples distributed according to the posterior distribution of the unknown parameters associated to this Bayesian Model. Simulation results conducted with synthetic data illustrate the performance of the proposed algorithm. The accuracy of this approach is also illustrated by unmixing spectra resulting from a multicomponent chemical mixture analysis by infrared spectroscopy.

  • Joint segmentation of piecewise constant autoregressive processes by using a Hierarchical Model and a Bayesian sampling approach
    IEEE Transactions on Signal Processing, 2007
    Co-Authors: Nicolas Dobigeon, Jean-yves Tourneret, Manuel Davy
    Abstract:

    We propose a joint segmentation algorithm for piecewise constant autoregressive (AR) processes recorded by several independent sensors. The algorithm is based on a Hierarchical Bayesian Model. Appropriate priors allow us to introduce correlations between the change locations of the observed signals. Numerical problems inherent to Bayesian inference are solved by a Gibbs sampling strategy. The proposed joint segmentation methodology yields improved segmentation results when compared with parallel and independent individual signal segmentations. The initial algorithm is derived for piecewise constant AR processes whose orders are fixed on each segment. However an extension to Models with unknown Model orders is also discussed. Theoretical results are illustrated by many simulations conducted with synthetic signals and real arc-tracking and speech signals.

Jean-yves Tourneret - One of the best experts on this subject based on the ideXlab platform.

  • Bayesian separation of spectral sources under non-negativity and full additivity constraints
    Signal Processing, 2009
    Co-Authors: Nicolas Dobigeon, Said Moussaoui, Jean-yves Tourneret
    Abstract:

    This paper addresses the problem of separating spectral sources which are linearly mixed with unknown proportions. The main difficulty of the problem is to ensure the full additivity (sum-to-one) of the mixing coefficients and non-negativity of sources and mixing coefficients. A Bayesian estimation approach based on Gamma priors was recently proposed to handle the non-negativity constraints in a linear mixture Model. However, incorporating the full additivity constraint requires further developments. This paper studies a new Hierarchical Bayesian Model appropriate to the non-negativity and sum-to-one constraints associated to the sources and the mixing coefficients of linear mixtures. The estimation of the unknown parameters of this Model is performed using samples obtained with an appropriate Gibbs algorithm. The performance of the proposed algorithm is evaluated through simulation results conducted on synthetic mixture data. The proposed approach is also applied to the processing of multicomponent chemical mixtures resulting from Raman spectroscopy.

  • Joint Bayesian Endmember Extraction and Linear Unmixing for Hyperspectral Imagery
    IEEE Transactions on Signal Processing, 2009
    Co-Authors: Nicolas Dobigeon, Jean-yves Tourneret, Said Moussaoui, Martial Coulon, Alfred O. Hero
    Abstract:

    This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing Model. The estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a Hierarchical Bayesian Model. This Model assumes conjugate prior distributions for these parameters, accounts for nonnegativity and full-additivity constraints, and exploits the fact that the endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution. This sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples. The accuracy of the joint Bayesian estimator is illustrated by simulations conducted on synthetic and real AVIRIS images.

  • Semi-Supervised Linear Spectral Unmixing Using a Hierarchical Bayesian Model for Hyperspectral Imagery
    IEEE Transactions on Signal Processing, 2008
    Co-Authors: Nicolas Dobigeon, Jean-yves Tourneret, Chein-i Chang
    Abstract:

    This paper proposes a Hierarchical Bayesian Model that can be used for semi-supervised hyperspectral image unmixing. The Model assumes that the pixel reflectances result from linear combinations of pure component spectra contaminated by an additive Gaussian noise. The abundance parameters appearing in this Model satisfy positivity and additivity constraints. These constraints are naturally expressed in a Bayesian context by using appropriate abundance prior distributions. The posterior distributions of the unknown Model parameters are then derived. A Gibbs sampler allows one to draw samples distributed according to the posteriors of interest and to estimate the unknown abundances. An extension of the algorithm is finally studied for mixtures with unknown numbers of spectral components belonging to a know library. The performance of the different unmixing strategies is evaluated via simulations conducted on synthetic and real data.

  • Blind unmixing of linear mixtures using a Hierarchical Bayesian Model. Application to spectroscopic signal analysis
    2007
    Co-Authors: Nicolas Dobigeon, Jean-yves Tourneret, Said Moussaoui
    Abstract:

    This paper addresses the problem of spectral unmixing when positivity and additivity constraints are imposed on the mixing coefficients. A Hierarchical Bayesian Model is introduced to satisfy these two constraints. A Gibbs sampler is then proposed to generate samples distributed according to the posterior distribution of the unknown parameters associated to this Bayesian Model. Simulation results conducted with synthetic data illustrate the performance of the proposed algorithm. The accuracy of this approach is also illustrated by unmixing spectra resulting from a multicomponent chemical mixture analysis by infrared spectroscopy.

  • Joint segmentation of piecewise constant autoregressive processes by using a Hierarchical Model and a Bayesian sampling approach
    IEEE Transactions on Signal Processing, 2007
    Co-Authors: Nicolas Dobigeon, Jean-yves Tourneret, Manuel Davy
    Abstract:

    We propose a joint segmentation algorithm for piecewise constant autoregressive (AR) processes recorded by several independent sensors. The algorithm is based on a Hierarchical Bayesian Model. Appropriate priors allow us to introduce correlations between the change locations of the observed signals. Numerical problems inherent to Bayesian inference are solved by a Gibbs sampling strategy. The proposed joint segmentation methodology yields improved segmentation results when compared with parallel and independent individual signal segmentations. The initial algorithm is derived for piecewise constant AR processes whose orders are fixed on each segment. However an extension to Models with unknown Model orders is also discussed. Theoretical results are illustrated by many simulations conducted with synthetic signals and real arc-tracking and speech signals.

Manuel Davy - One of the best experts on this subject based on the ideXlab platform.

Costas Papadimitriou - One of the best experts on this subject based on the ideXlab platform.

  • accounting for amplitude of excitation in Model updating through a Hierarchical Bayesian approach application to a two story reinforced concrete building
    Mechanical Systems and Signal Processing, 2019
    Co-Authors: Mingming Song, Babak Moaveni, Costas Papadimitriou, Andreas Stavridis
    Abstract:

    Abstract Calibrated linear equivalent Models of civil structures are often used for response prediction and performance assessment. However, these Models are only valid for a narrow range of excitation level for which these Models are calibrated. In this paper a Hierarchical Bayesian Model updating approach is proposed for Model calibration and response prediction of dynamic structural systems in a wide range of excitation levels where the linear equivalent stiffness of different structural components are updated as functions of excitation amplitude. The proposed approach is implemented on a two-story reinforced concrete building with masonry infills. The building, located in El Centro California, has suffered severe damage during past earthquakes. Ambient and forced vibration tests were performed on the building using an eccentric mass shaker, and its dynamic response was measured using an array of accelerometers. The modal parameters of the structure are identified under different amplitudes of vibration and the natural frequencies exhibit significant decrease at higher vibration levels. The Hierarchical Bayesian Model updating approach is used to estimate the probability distribution of effective stiffness of considered structural components which is characterized by the stiffness mean and covariance as hyperparameters, as well as Modeling errors. To account for the effect of vibration amplitude, the effective stiffness mean is considered as a function of vibration level. A two-step sampling approach is proposed to evaluate the joint posterior probability distribution of updating parameters. The calibrated Model is then used to predict time history response of the building under forced vibration which is compared with measured data. The good agreement observed from this comparison verifies the calibrated Model and the proposed approach to account for the excitation level in updating process.

  • Modeling Error Estimation and Response Prediction of a 10-Story Building Model Through a Hierarchical Bayesian Model Updating Framework
    Frontiers Media S.A., 2019
    Co-Authors: Mingming Song, Iman Behmanesh, Babak Moaveni, Costas Papadimitriou
    Abstract:

    In this paper a Hierarchical Bayesian Model updating approach is proposed for calibration of Model parameters, estimation of Modeling error, and response prediction of dynamic structural systems. The approach is especially suitable for civil structural systems where Modeling errors are usually significant. The proposed framework is demonstrated through a numerical case study, namely a 10-story building Model. The “measured data” include the numerically simulated modal parameters of a frame Model which represents the true structure. A simplified shear building Model with significant Modeling errors is then considered for Model updating with stiffness of different structural components (substructures) chosen as updating parameters. In the proposed Hierarchical Bayesian framework, updating parameters are assumed to follow a known distribution Model (normal distribution is considered here) and are characterized by the distribution parameters (mean vector and covariance matrix). The error function, which is defined as the misfit between Model-predicted and identified modal parameters, is also assumed to follow a normal distribution with unknown parameters. The Hierarchical Bayesian approach is applied to estimate the stiffness parameter distributions with mean and covariance matrix referred to as hyperparameters, as well as the Modeling error which is quantified by the mean and covariance of error function. Joint posterior probability distribution of all updating parameters is derived from the likelihood function and the prior distributions. A Metropolis-Hastings within Gibbs sampler is implemented to evaluate the joint posterior distribution numerically. Two cases of Model updating are studied with first case assuming a zero mean for the error function, and the second case considering a non-zero error mean. The response time history of the building to a ground motion is predicted using the calibrated shear building Model for both cases and compared with the exact response (simulated). Good agreements between predictions and measurements are observed for both cases with better accuracy in the second case. This verifies the proposed Hierarchical Bayesian approach for Model calibration and response prediction and underlines the importance of considering and propagating the uncertainties of structural parameters and more importantly Modeling errors

  • Hierarchical Bayesian Model updating for structural identification
    Mechanical Systems and Signal Processing, 2015
    Co-Authors: Iman Behmanesh, Babak Moaveni, Geert Lombaert, Costas Papadimitriou
    Abstract:

    Abstract A new probabilistic finite element (FE) Model updating technique based on Hierarchical Bayesian Modeling is proposed for identification of civil structural systems under changing ambient/environmental conditions. The performance of the proposed technique is investigated for (1) uncertainty quantification of Model updating parameters, and (2) probabilistic damage identification of the structural systems. Accurate estimation of the uncertainty in Modeling parameters such as mass or stiffness is a challenging task. Several Bayesian Model updating frameworks have been proposed in the literature that can successfully provide the “parameter estimation uncertainty” of Model parameters with the assumption that there is no underlying inherent variability in the updating parameters. However, this assumption may not be valid for civil structures where structural mass and stiffness have inherent variability due to different sources of uncertainty such as changing ambient temperature, temperature gradient, wind speed, and traffic loads. Hierarchical Bayesian Model updating is capable of predicting the overall uncertainty/variability of updating parameters by assuming time-variability of the underlying linear system. A general solution based on Gibbs Sampler is proposed to estimate the joint probability distributions of the updating parameters. The performance of the proposed Hierarchical approach is evaluated numerically for uncertainty quantification and damage identification of a 3-story shear building Model. Effects of Modeling errors and incomplete modal data are considered in the numerical study.

Fernando Colchero - One of the best experts on this subject based on the ideXlab platform.

  • better the devil you know common terns stay with a previous partner although pair bond duration does not affect breeding output
    Proceedings of The Royal Society B: Biological Sciences, 2017
    Co-Authors: Maren Rebke, Peter H Becker, Fernando Colchero
    Abstract:

    In a monogamous species two partners contribute to the breeding process. We study pair formation as well as the effect of pair bond length and age on breeding performance, incorporating individual heterogeneity, based on a high-quality dataset of a long-lived seabird, the common tern ( Sterna hirundo ). To handle missing information and Model the complicated processes driving reproduction, we use a Hierarchical Bayesian Model of the steps that lead to the number of fledglings, including processes at the individual and the pair level. The results show that the age of both partners is important for reproductive performance, with similar patterns for both sexes and individual heterogeneity in reproductive performance, but pair bond length is not. The terns are more likely to choose a former partner independent of the previous breeding outcome with that partner, which suggests a tendency to retain the partner chosen at the beginning of the breeding career.