arXiv subjects

Nicolas Dobigeon

Publications and source records attributed to Nicolas Dobigeon.

At least 73 records · Page 4Linked to original sources

arXiv2015

Fast Spectral Unmixing based on Dykstra's Alternating Projection

This paper presents a fast spectral unmixing algorithm based on Dykstra's alternating projection. The proposed algorithm formulates the fully constrained least squares optimization problem associated with the spectral unmixing task as an unconstrained regression problem followed by a projection onto the intersection of several closed convex sets. This projection is achieved by iteratively projecting onto each of the convex sets individually, following Dyktra's scheme. The sequence thus obtained is guaranteed to converge to the sought projection. Thanks to the preliminary matrix decomposition and variable substitution, the projection is implemented intrinsically in a subspace, whose dimension is very often much lower than the number of bands. A benefit of this strategy is that the order of the computational complexity for each projection is decreased from quadratic to linear time. Numerical experiments considering diverse spectral unmixing scenarios provide evidence that the proposed algorithm competes with the state-of-the-art, namely when the number of endmembers is relatively small, a circumstance often observed in real hyperspectral applications.

cs.CV↗

arXiv2015

Hyperspectral pansharpening: a review

Pansharpening aims at fusing a panchromatic image with a multispectral one, to generate an image with the high spatial resolution of the former and the high spectral resolution of the latter. In the last decade, many algorithms have been presented in the literature for pansharpening using multispectral data. With the increasing availability of hyperspectral systems, these methods are now being adapted to hyperspectral images. In this work, we compare new pansharpening techniques designed for hyperspectral data with some of the state of the art methods for multispectral pansharpening, which have been adapted for hyperspectral data. Eleven methods from different classes (component substitution, multiresolution analysis, hybrid, Bayesian and matrix factorization) are analyzed. These methods are applied to three datasets and their effectiveness and robustness are evaluated with widely used performance indicators. In addition, all the pansharpening techniques considered in this paper have been implemented in a MATLAB toolbox that is made available to the community.

cs.CV↗

arXiv2015

Bayesian estimation of the multifractality parameter for image texture using a Whittle approximation

Texture characterization is a central element in many image processing applications. Multifractal analysis is a useful signal and image processing tool, yet, the accurate estimation of multifractal parameters for image texture remains a challenge. This is due in the main to the fact that current estimation procedures consist of performing linear regressions across frequency scales of the two-dimensional (2D) dyadic wavelet transform, for which only a few such scales are computable for images. The strongly non-Gaussian nature of multifractal processes, combined with their complicated dependence structure, makes it difficult to develop suitable models for parameter estimation. Here, we propose a Bayesian procedure that addresses the difficulties in the estimation of the multifractality parameter. The originality of the procedure is threefold: The construction of a generic semi-parametric statistical model for the logarithm of wavelet leaders; the formulation of Bayesian estimators that are associated with this model and the set of parameter values admitted by multifractal theory; the exploitation of a suitable Whittle approximation within the Bayesian model which enables the otherwise infeasible evaluation of the posterior distribution associated with the model. Performance is assessed numerically for several 2D multifractal processes, for several image sizes and a large range of process parameters. The procedure yields significant benefits over current benchmark estimators in terms of estimation performance and ability to discriminate between the two most commonly used classes of multifractal process models. The gains in performance are particularly pronounced for small image sizes, notably enabling for the first time the analysis of image patches as small as 64x64 pixels.

physics.data-an↗

arXiv2015

Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation

This paper proposes a fast multi-band image fusion algorithm, which combines a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. The well admitted forward model is explored to form the likelihoods of the observations. Maximizing the likelihoods leads to solving a Sylvester equation. By exploiting the properties of the circulant and downsampling matrices associated with the fusion problem, a closed-form solution for the corresponding Sylvester equation is obtained explicitly, getting rid of any iterative update step. Coupled with the alternating direction method of multipliers and the block coordinate descent method, the proposed algorithm can be easily generalized to incorporate prior information for the fusion problem, allowing a Bayesian estimator. Simulation results show that the proposed algorithm achieves the same performance as existing algorithms with the advantage of significantly decreasing the computational complexity of these algorithms.

cs.CV↗

arXiv2014

Hyperspectral and Multispectral Image Fusion based on a Sparse Representation

This paper presents a variational based approach to fusing hyperspectral and multispectral images. The fusion process is formulated as an inverse problem whose solution is the target image assumed to live in a much lower dimensional subspace. A sparse regularization term is carefully designed, relying on a decomposition of the scene on a set of dictionaries. The dictionary atoms and the corresponding supports of active coding coefficients are learned from the observed images. Then, conditionally on these dictionaries and supports, the fusion problem is solved via alternating optimization with respect to the target image (using the alternating direction method of multipliers) and the coding coefficients. Simulation results demonstrate the efficiency of the proposed algorithm when compared with the state-of-the-art fusion methods.

cs.CV↗

arXiv2014

Bayesian Fusion of Multi-Band Images

In this paper, a Bayesian fusion technique for remotely sensed multi-band images is presented. The observed images are related to the high spectral and high spatial resolution image to be recovered through physical degradations, e.g., spatial and spectral blurring and/or subsampling defined by the sensor characteristics. The fusion problem is formulated within a Bayesian estimation framework. An appropriate prior distribution exploiting geometrical consideration is introduced. To compute the Bayesian estimator of the scene of interest from its posterior distribution, a Markov chain Monte Carlo algorithm is designed to generate samples asymptotically distributed according to the target distribution. To efficiently sample from this high-dimension distribution, a Hamiltonian Monte Carlo step is introduced in the Gibbs sampling strategy. The efficiency of the proposed fusion method is evaluated with respect to several state-of-the-art fusion techniques. In particular, low spatial resolution hyperspectral and multispectral images are fused to produce a high spatial resolution hyperspectral image.

cs.CV↗

arXiv2014

Unsupervised Unmixing of Hyperspectral Images Accounting for Endmember Variability

This paper presents an unsupervised Bayesian algorithm for hyperspectral image unmixing accounting for endmember variability. The pixels are modeled by a linear combination of endmembers weighted by their corresponding abundances. However, the endmembers are assumed random to take into account their variability in the image. An additive noise is also considered in the proposed model generalizing the normal compositional model. The proposed algorithm exploits the whole image to provide spectral and spatial information. It estimates both the mean and the covariance matrix of each endmember in the image. This allows the behavior of each material to be analyzed and its variability to be quantified in the scene. A spatial segmentation is also obtained based on the estimated abundances. In order to estimate the parameters associated with the proposed Bayesian model, we propose to use a Hamiltonian Monte Carlo algorithm. The performance of the resulting unmixing strategy is evaluated via simulations conducted on both synthetic and real data.

stat.ME↗

arXiv2014

A comparison of nonlinear mixing models for vegetated areas using simulated and real hyperspectral data

Spectral unmixing is a crucial processing step when analyzing hyperspectral data. In such analysis, most of the work in the literature relies on the widely acknowledged linear mixing model to describe the observed pixels. Unfortunately, this model has been shown to be of limited interest for specific scenes, in particular when acquired over vegetated areas. Consequently, in the past few years, several nonlinear mixing models have been introduced to take nonlinear effects into account while performing spectral unmixing. These models have been proposed empirically, however without any thorough validation. In this paper, the authors take advantage of two sets of real and physical-based simulated data to validate the accuracy of various nonlinear models in vegetated areas. These physics-based and analysis models, and their corresponding unmixing algorithms, are evaluated with respect to their ability of fitting the measured spectra and of providing an accurate estimation of the abundance coefficients, considered as the spatial distribution of the materials in each pixel.

physics.data-an↗

arXiv2014

Nonlinear hyperspectral unmixing with robust nonnegative matrix factorization

This paper introduces a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures. This new model not only generalizes the commonly used linear mixing model, but also allows for possible nonlinear effects to be easily handled, relying on mild assumptions regarding these nonlinearities. The standard nonnegativity and sum-to-one constraints inherent to spectral unmixing are coupled with a group-sparse constraint imposed on the nonlinearity component. This results in a new form of robust nonnegative matrix factorization. The data fidelity term is expressed as a beta-divergence, a continuous family of dissimilarity measures that takes the squared Euclidean distance and the generalized Kullback-Leibler divergence as special cases. The penalized objective is minimized with a block-coordinate descent that involves majorization-minimization updates. Simulation results obtained on synthetic and real data show that the proposed strategy competes with state-of-the-art linear and nonlinear unmixing methods.

stat.ME↗

arXiv2013

A normalized scaled gradient method to solve non-negativity and equality constrained linear inverse problem - Application to spectral mixture analysis

This paper addresses the problem of minimizing a convex cost function under non-negativity and equality constraints, with the aim of solving the linear unmixing problem encountered in hyperspectral imagery. This problem can be formulated as a linear regression problem whose regression coefficients (abundances) satisfy sum-to-one and positivity constraints. A normalized scaled gradient iterative method (NSGM) is proposed for estimating the abundances of the linear mixing model. The positivity constraint is ensured by the Karush Kuhn Tucker conditions whereas the sum-to-one constraint is fulfilled by introducing normalized variables in the algorithm. The convergence is ensured by a one-dimensional search of the step size. Note that NSGM can be applied to any convex cost function with non negativity and flux constraints. In order to compare the NSGM with the well-known fully constraint least squares (FCLS) algorithm, this latter is reformulated in term of a penalized function, which reveals its suboptimality. Simulations on synthetic data illustrate the performances of the proposed algorithm in comparison with other unmixing algorithms and, more particulary, demonstrate its efficiency when compared to the popular FCLS. Finally, results on real data are given.

math.OC↗

arXiv2013

Joint Bayesian estimation of close subspaces from noisy measurements

In this letter, we consider two sets of observations defined as subspace signals embedded in noise and we wish to analyze the distance between these two subspaces. The latter entails evaluating the angles between the subspaces, an issue reminiscent of the well-known Procrustes problem. A Bayesian approach is investigated where the subspaces of interest are considered as random with a joint prior distribution (namely a Bingham distribution), which allows the closeness of the two subspaces to be adjusted. Within this framework, the minimum mean-square distance estimator of both subspaces is formulated and implemented via a Gibbs sampler. A simpler scheme based on alternative maximum a posteriori estimation is also presented. The new schemes are shown to provide more accurate estimates of the angles between the subspaces, compared to singular value decomposition based independent estimation of the two subspaces.

stat.ME↗

arXiv2013

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.

stat.CO↗

arXiv2013

Residual component analysis of hyperspectral images -- Application to joint nonlinear unmixing and nonlinearity detection

This paper presents a nonlinear mixing model for joint hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are linear combinations of known pure spectral components corrupted by an additional nonlinear term, affecting the endmembers and contaminated by an additive Gaussian noise. A Markov random field is considered for nonlinearity detection based on the spatial structure of the nonlinear terms. The observed image is segmented into regions where nonlinear terms, if present, share similar statistical properties. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding a joint nonlinear unmixing and nonlinearity detection algorithm. The performance of the proposed strategy is first evaluated on synthetic data. Simulations conducted with real data show the accuracy of the proposed unmixing and nonlinearity detection strategy for the analysis of hyperspectral images.

stat.ME↗

arXiv2013

Nonlinear unmixing of hyperspectral images: models and algorithms

When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear models need to be considered, for instance, when there are multi-scattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this paper, we present an overview of recent advances in nonlinear unmixing modeling.

physics.data-an↗

arXiv2013

Unsupervised Post-Nonlinear Unmixing of Hyperspectral Images Using a Hamiltonian Monte Carlo Algorithm

This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are post-nonlinear functions of unknown pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomials leading to a polynomial post-nonlinear mixing model. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding an unsupervised nonlinear unmixing algorithm. Due to the large number of parameters to be estimated, an efficient Hamiltonian Monte Carlo algorithm is investigated. The classical leapfrog steps of this algorithm are modified to handle the parameter constraints. The performance of the unmixing strategy, including convergence and parameter tuning, is first evaluated on synthetic data. Simulations conducted with real data finally show the accuracy of the proposed unmixing strategy for the analysis of hyperspectral images.

stat.ME↗

arXiv2013

Variational Semi-blind Sparse Deconvolution with Orthogonal Kernel Bases and its Application to MRFM

We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM).

physics.data-an↗

arXiv2012

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.

stat.ME↗

arXiv2012

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.

stat.CO↗