Estimating the granularity coefficient of a Potts-Markov random field within an MCMC algorithm

This paper addresses the problem of estimating the Potts parameter B jointly with the unknown parameters of a Bayesian model within a Markov chain Monte Carlo (MCMC) algorithm. Standard MCMC methods cannot be applied to this problem because performing inference on B requires computing the intractable normalizing constant of the Potts model. In the proposed MCMC method the estimation of B is conducted using a likelihood-free Metropolis-Hastings algorithm. Experimental results obtained for synthetic data show that estimating B jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of B. On the other hand, assuming that the value of B is known can degrade estimation performance significantly if this value is incorrect. To illustrate the interest of this method, the proposed algorithm is successfully applied to real bidimensional SAR and tridimensional ultrasound images

Computing the Cramer-Rao bound of Markov random field parameters: Application to the Ising and the Potts models

This report considers the problem of computing the Cramer-Rao bound for the parameters of a Markov random field. Computation of the exact bound is not feasible for most fields of interest because their likelihoods are intractable and have intractable derivatives. We show here how it is possible to formulate the computation of the bound as a statistical inference problem that can be solve approximately, but with arbitrarily high accuracy, by using a Monte Carlo method. The proposed methodology is successfully applied on the Ising and the Potts models.% where it is used to assess the performance of three state-of-the art estimators of the parameter of these Markov random fields

Enhancing hyperspectral image unmixing with spatial correlations

This paper describes a new algorithm for hyperspectral image unmixing. Most of the unmixing algorithms proposed in the literature do not take into account the possible spatial correlations between the pixels. In this work, a Bayesian model is introduced to exploit these correlations. The image to be unmixed is assumed to be partitioned into regions (or classes) where the statistical properties of the abundance coefficients are homogeneous. A Markov random field is then proposed to model the spatial dependency of the pixels within any class. Conditionally upon a given class, each pixel is modeled by using the classical linear mixing model with additive white Gaussian noise. This strategy is investigated the well known linear mixing model. For this model, the posterior distributions of the unknown parameters and hyperparameters allow ones to infer the parameters of interest. These parameters include the abundances for each pixel, the means and variances of the abundances for each class, as well as a classification map indicating the classes of all pixels in the image. To overcome the complexity of the posterior distribution of interest, we consider Markov chain Monte Carlo methods that generate samples distributed according to the posterior of interest. The generated samples are then used for parameter and hyperparameter estimation. The accuracy of the proposed algorithms is illustrated on synthetic and real data.Comment: Manuscript accepted for publication in IEEE Trans. Geoscience and Remote Sensin

Robust Linear Spectral Unmixing using Anomaly Detection

This paper presents a Bayesian algorithm for linear spectral unmixing of hyperspectral images that accounts for anomalies present in the data. The model proposed assumes that the pixel reflectances are linear mixtures of unknown endmembers, corrupted by an additional nonlinear term modelling anomalies and additive Gaussian noise. A Markov random field is used for anomaly detection based on the spatial and spectral structures of the anomalies. This allows outliers to be identified in particular regions and wavelengths of the data cube. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding a joint linear unmixing and anomaly detection algorithm. Simulations conducted with synthetic and real hyperspectral images demonstrate the accuracy of the proposed unmixing and outlier detection strategy for the analysis of hyperspectral images

Lidar waveform based analysis of depth images constructed using sparse single-photon data

This paper presents a new Bayesian model and algorithm used for depth and intensity profiling using full waveforms from the time-correlated single photon counting (TCSPC) measurement in the limit of very low photon counts. The model proposed represents each Lidar waveform as a combination of a known impulse response, weighted by the target intensity, and an unknown constant background, corrupted by Poisson noise. Prior knowledge about the problem is embedded in a hierarchical model that describes the dependence structure between the model parameters and their constraints. In particular, a gamma Markov random field (MRF) is used to model the joint distribution of the target intensity, and a second MRF is used to model the distribution of the target depth, which are both expected to exhibit significant spatial correlations. An adaptive Markov chain Monte Carlo algorithm is then proposed to compute the Bayesian estimates of interest and perform Bayesian inference. This algorithm is equipped with a stochastic optimization adaptation mechanism that automatically adjusts the parameters of the MRFs by maximum marginal likelihood estimation. Finally, the benefits of the proposed methodology are demonstrated through a serie of experiments using real data

Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing

This paper presents a new Bayesian collaborative sparse regression method for linear unmixing of hyperspectral images. Our contribution is twofold; first, we propose a new Bayesian model for structured sparse regression in which the supports of the sparse abundance vectors are a priori spatially correlated across pixels (i.e., materials are spatially organised rather than randomly distributed at a pixel level). This prior information is encoded in the model through a truncated multivariate Ising Markov random field, which also takes into consideration the facts that pixels cannot be empty (i.e, there is at least one material present in each pixel), and that different materials may exhibit different degrees of spatial regularity. Secondly, we propose an advanced Markov chain Monte Carlo algorithm to estimate the posterior probabilities that materials are present or absent in each pixel, and, conditionally to the maximum marginal a posteriori configuration of the support, compute the MMSE estimates of the abundance vectors. A remarkable property of this algorithm is that it self-adjusts the values of the parameters of the Markov random field, thus relieving practitioners from setting regularisation parameters by cross-validation. The performance of the proposed methodology is finally demonstrated through a series of experiments with synthetic and real data and comparisons with other algorithms from the literature

Robust Bayesian target detection algorithm for depth imaging from sparse single-photon data

This paper presents a new Bayesian model and associated algorithm for depth and intensity profiling using full waveforms from time-correlated single-photon counting (TCSPC) measurements in the limit of very low photon counts (i.e., typically less than 20 photons per pixel). The model represents each Lidar waveform as an unknown constant background level, which is combined in the presence of a target, to a known impulse response weighted by the target intensity and finally corrupted by Poisson noise. The joint target detection and depth imaging problem is expressed as a pixel-wise model selection and estimation problem which is solved using Bayesian inference. Prior knowledge about the problem is embedded in a hierarchical model that describes the dependence structure between the model parameters while accounting for their constraints. In particular, Markov random fields (MRFs) are used to model the joint distribution of the background levels and of the target presence labels, which are both expected to exhibit significant spatial correlations. An adaptive Markov chain Monte Carlo algorithm including reversible-jump updates is then proposed to compute the Bayesian estimates of interest. This algorithm is equipped with a stochastic optimization adaptation mechanism that automatically adjusts the parameters of the MRFs by maximum marginal likelihood estimation. Finally, the benefits of the proposed methodology are demonstrated through a series of experiments using real data.Comment: arXiv admin note: text overlap with arXiv:1507.0251

Bayesian nonlinear hyperspectral unmixing with spatial residual component analysis

This paper presents a new Bayesian model and algorithm for nonlinear unmixing of hyperspectral images. The model proposed represents the pixel reflectances as linear combinations of the endmembers, corrupted by nonlinear (with respect to the endmembers) terms and additive Gaussian noise. Prior knowledge about the problem is embedded in a hierarchical model that describes the dependence structure between the model parameters and their constraints. In particular, a gamma Markov random field is used to model the joint distribution of the nonlinear terms, which are expected to exhibit significant spatial correlations. An adaptive Markov chain Monte Carlo algorithm is then proposed to compute the Bayesian estimates of interest and perform Bayesian inference. This algorithm is equipped with a stochastic optimisation adaptation mechanism that automatically adjusts the parameters of the gamma Markov random field by maximum marginal likelihood estimation. Finally, the proposed methodology is demonstrated through a series of experiments with comparisons using synthetic and real data and with competing state-of-the-art approaches