arXiv subjects

Jean-Yves Tourneret

Publications and source records attributed to Jean-Yves Tourneret.

At least 37 records · Page 2Linked to original sources

arXiv2017

EEG reconstruction and skull conductivity estimation using a Bayesian model promoting structured sparsity

M/EEG source localization is an open research issue. To solve it, it is important to have good knowledge of several physical parameters to build a reliable head operator. Amongst them, the value of the conductivity of the human skull has remained controversial. This report introduces a novel hierarchical Bayesian framework to estimate the skull conductivity jointly with the brain activity from the M/EEG measurements to improve the reconstruction quality. A partially collapsed Gibbs sampler is used to draw samples asymptotically distributed according to the associated posterior. The generated samples are then used to estimate the brain activity and the model hyperparameters jointly in a completely unsupervised framework. We use synthetic and real data to illustrate the improvement of the reconstruction. The performance of our method is also compared with two optimization algorithms introduced by Vallaghé \textit{et al.} and Gutierrez \textit{et al.} respectively, showing that our method is able to provide results of similar or better quality while remaining applicable in a wider array of situations.

stat.ME↗

arXiv2016

A Bayesian Lower Bound for Parameter Estimation of Poisson Data Including Multiple Changes (extended)

This paper derives lower bounds for the mean square errors of parameter estimators in the case of Poisson distributed data subjected to multiple abrupt changes. Since both change locations (discrete parameters) and parameters of the Poisson distribution (continuous parameters) are unknown, it is appropriate to consider a mixed Cramer-Rao/Weiss-Weinstein bound for which we derive closed-form expressions and illustrate its tightness by numerical simulations.

cs.IT↗

arXiv2016

Online Unmixing of Multitemporal Hyperspectral Images accounting for Spectral Variability

Hyperspectral unmixing is aimed at identifying the reference spectral signatures composing an hyperspectral image and their relative abundance fractions in each pixel. In practice, the identified signatures may vary spectrally from an image to another due to varying acquisition conditions, thus inducing possibly significant estimation errors. Against this background, hyperspectral unmixing of several images acquired over the same area is of considerable interest. Indeed, such an analysis enables the endmembers of the scene to be tracked and the corresponding endmember variability to be characterized. Sequential endmember estimation from a set of hyperspectral images is expected to provide improved performance when compared to methods analyzing the images independently. However, the significant size of hyperspectral data precludes the use of batch procedures to jointly estimate the mixture parameters of a sequence of hyperspectral images. Provided that each elementary component is present in at least one image of the sequence, we propose to perform an online hyperspectral unmixing accounting for temporal endmember variability. The online hyperspectral unmixing is formulated as a two-stage stochastic program, which can be solved using a stochastic approximation. The performance of the proposed method is evaluated on synthetic and real data. A comparison with independent unmixing algorithms finally illustrates the interest of the proposed strategy.

physics.data-an↗

arXiv2016

Joint Segmentation and Deconvolution of Ultrasound Images Using a Hierarchical Bayesian Model based on Generalized Gaussian Priors

This paper proposes a joint segmentation and deconvolution Bayesian method for medical ultrasound (US) images. Contrary to piecewise homogeneous images, US images exhibit heavy characteristic speckle patterns correlated with the tissue structures. The generalized Gaussian distribution (GGD) has been shown to be one of the most relevant distributions for characterizing the speckle in US images. Thus, we propose a GGD-Potts model defined by a label map coupling US image segmentation and deconvolution. The Bayesian estimators of the unknown model parameters, including the US image, the label map and all the hyperparameters are difficult to be expressed in closed form. Thus, we investigate a Gibbs sampler to generate samples distributed according to the posterior of interest. These generated samples are finally used to compute the Bayesian estimators of the unknown parameters. The performance of the proposed Bayesian model is compared with existing approaches via several experiments conducted on realistic synthetic data and in vivo US images.

cs.CV↗

arXiv2016

Fast Single Image Super-Resolution

This paper addresses the problem of single image super-resolution (SR), which consists of recovering a high resolution image from its blurred, decimated and noisy version. The existing algorithms for single image SR use different strategies to handle the decimation and blurring operators. In addition to the traditional first-order gradient methods, recent techniques investigate splitting-based methods dividing the SR problem into up-sampling and deconvolution steps that can be easily solved. Instead of following this splitting strategy, we propose to deal with the decimation and blurring operators simultaneously by taking advantage of their particular properties in the frequency domain, leading to a new fast SR approach. Specifically, an analytical solution can be obtained and implemented efficiently for the Gaussian prior or any other regularization that can be formulated into an $\ell_2$-regularized quadratic model, i.e., an $\ell_2$-$\ell_2$ optimization problem. Furthermore, the flexibility of the proposed SR scheme is shown through the use of various priors/regularizations, ranging from generic image priors to learning-based approaches. In the case of non-Gaussian priors, we show how the analytical solution derived from the Gaussian case can be embedded intotraditional splitting frameworks, allowing the computation cost of existing algorithms to be decreased significantly. Simulation results conducted on several images with different priors illustrate the effectiveness of our fast SR approach compared with the existing techniques.

cs.CV↗

arXiv2016

Unsupervised Nonlinear Spectral Unmixing based on a Multilinear Mixing Model

In the community of remote sensing, nonlinear mixing models have recently received particular attention in hyperspectral image processing. In this paper, we present a novel nonlinear spectral unmixing method following the recent multilinear mixing model of [1], which includes an infinite number of terms related to interactions between different endmembers. The proposed unmixing method is unsupervised in the sense that the endmembers are estimated jointly with the abundances and other parameters of interest, i.e., the transition probability of undergoing further interactions. Non-negativity and sum-to one constraints are imposed on abundances while only nonnegativity is considered for endmembers. The resulting unmixing problem is formulated as a constrained nonlinear optimization problem, which is solved by a block coordinate descent strategy, consisting of updating the endmembers, abundances and transition probability iteratively. The proposed method is evaluated and compared with linear unmixing methods for synthetic and real hyperspectral datasets acquired by the AVIRIS sensor. The advantage of using non-linear unmixing as opposed to linear unmixing is clearly shown in these examples.

cs.CV↗

arXiv2016

R-FUSE: Robust Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation

This paper proposes a robust fast multi-band image fusion method to merge a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. Following the method recently developed in [1], the generalized Sylvester matrix equation associated with the multi-band image fusion problem is solved in a more robust and efficient way by exploiting the Woodbury formula, avoiding any permutation operation in the frequency domain as well as the blurring kernel invertibility assumption required in [1]. Thanks to this improvement, the proposed algorithm requires fewer computational operations and is also more robust with respect to the blurring kernel compared with the one in [1]. The proposed new algorithm is tested with different priors considered in [1]. Our conclusion is that the proposed fusion algorithm is more robust than the one in [1] with a reduced computational cost.

cs.CV↗

arXiv2016

Multi-Band Image Fusion Based on Spectral Unmixing

This paper presents a multi-band image fusion algorithm based on unsupervised spectral unmixing for combining a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. The widely used linear observation model (with additive Gaussian noise) is combined with the linear spectral mixture model to form the likelihoods of the observations. The non-negativity and sum-to-one constraints resulting from the intrinsic physical properties of the abundances are introduced as prior information to regularize this ill-posed problem. The joint fusion and unmixing problem is then formulated as maximizing the joint posterior distribution with respect to the endmember signatures and abundance maps, This optimization problem is attacked with an alternating optimization strategy. The two resulting sub-problems are convex and are solved efficiently using the alternating direction method of multipliers. Experiments are conducted for both synthetic and semi-real data. Simulation results show that the proposed unmixing based fusion scheme improves both the abundance and endmember estimation comparing with the state-of-the-art joint fusion and unmixing algorithms.

cs.CV↗

arXiv2015

A Survey of Stochastic Simulation and Optimization Methods in Signal Processing

Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational inference techniques. This has driven the development of statistical SP methods based on stochastic simulation and optimization. Stochastic simulation and optimization algorithms are computationally intensive tools for performing statistical inference in models that are analytically intractable and beyond the scope of deterministic inference methods. They have been recently successfully applied to many difficult problems involving complex statistical models and sophisticated (often Bayesian) statistical inference techniques. This survey paper offers an introduction to stochastic simulation and optimization methods in signal and image processing. The paper addresses a variety of high-dimensional Markov chain Monte Carlo (MCMC) methods as well as deterministic surrogate methods, such as variational Bayes, the Bethe approach, belief and expectation propagation and approximate message passing algorithms. It also discusses a range of optimization methods that have been adopted to solve stochastic problems, as well as stochastic methods for deterministic optimization. Subsequently, areas of overlap between simulation and optimization, in particular optimization-within-MCMC and MCMC-driven optimization are discussed.

cs.IT↗

arXiv2015

Hyperspectral unmixing with spectral variability using a perturbed linear mixing model

Given a mixed hyperspectral data set, linear unmixing aims at estimating the reference spectral signatures composing the data - referred to as endmembers - their abundance fractions and their number. In practice, the identified endmembers can vary spectrally within a given image and can thus be construed as variable instances of reference endmembers. Ignoring this variability induces estimation errors that are propagated into the unmixing procedure. To address this issue, endmember variability estimation consists of estimating the reference spectral signatures from which the estimated endmembers have been derived as well as their variability with respect to these references. This paper introduces a new linear mixing model that explicitly accounts for spatial and spectral endmember variabilities. The parameters of this model can be estimated using an optimization algorithm based on the alternating direction method of multipliers. The performance of the proposed unmixing method is evaluated on synthetic and real data. A comparison with state-of-the-art algorithms designed to model and estimate endmember variability allows the interest of the proposed unmixing solution to be appreciated.

stat.ME↗

arXiv2015

Bayesian Structured Sparsity Priors for EEG Source Localization Technical Report

This report introduces a new hierarchical Bayesian model for the EEG source localization problem. This model promotes structured sparsity to search for focal brain activity. This sparsity is obtained via a multivariate Bernoulli Laplacian prior assigned to the brain activity approximating an $\ell_{20}$ pseudo norm regularization in a Bayesian framework. A partially collapsed Gibbs sampler is used to draw samples asymptotically distributed according to the posterior associated with the proposed Bayesian model. The generated samples are used to estimate the brain activity and the model hyperparameters jointly in an unsupervised framework. Two different kinds of Metropolis-Hastings moves are introduced to accelerate the convergence of the Gibbs sampler. The first move is based on multiple dipole shifts within each MCMC chain whereas the second one exploits proposals associated with different MCMC chains. We use both synthetic and real data to compare the performance of the proposed method with the weighted $\ell_{21}$ mixed norm regularization and a method based on a multiple sparse prior, showing that our algorithm presents advantages in several scenarios.

stat.ME↗

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

Nonparametric Detection of Nonlinearly Mixed Pixels and Endmember Estimation in Hyperspectral Images

Mixing phenomena in hyperspectral images depend on a variety of factors such as the resolution of observation devices, the properties of materials, and how these materials interact with incident light in the scene. Different parametric and nonparametric models have been considered to address hyperspectral unmixing problems. The simplest one is the linear mixing model. Nevertheless, it has been recognized that mixing phenomena can also be nonlinear. The corresponding nonlinear analysis techniques are necessarily more challenging and complex than those employed for linear unmixing. Within this context, it makes sense to detect the nonlinearly mixed pixels in an image prior to its analysis, and then employ the simplest possible unmixing technique to analyze each pixel. In this paper, we propose a technique for detecting nonlinearly mixed pixels. The detection approach is based on the comparison of the reconstruction errors using both a Gaussian process regression model and a linear regression model. The two errors are combined into a detection statistics for which a probability density function can be reasonably approximated. We also propose an iterative endmember extraction algorithm to be employed in combination with the detection algorithm. The proposed Detect-then-Unmix strategy, which consists of extracting endmembers, detecting nonlinearly mixed pixels and unmixing, is tested with synthetic and real images.

cs.CV↗

arXiv2015

Bayesian Estimation of Smooth Altimetric Parameters: Application to Conventional and Delay/Doppler Altimetry

This paper proposes a new Bayesian strategy for the smooth estimation of altimetric parameters. The altimetric signal is assumed to be corrupted by a thermal and speckle noise distributed according to an independent and non identically Gaussian distribution. We introduce a prior enforcing a smooth temporal evolution of the altimetric parameters which improves their physical interpretation. The posterior distribution of the resulting model is optimized using a gradient descent algorithm which allows us to compute the maximum a posteriori estimator of the unknown model parameters. This algorithm presents a low computational cost which is suitable for real time applications. The proposed Bayesian strategy and the corresponding estimation algorithm are validated on both synthetic and real data associated with conventional and delay/Doppler altimetry. The analysis of real Jason-2 and Cryosat-2 waveforms shows an improvement in parameter estimation when compared to the state-of-the-art estimation algorithms.

stat.AP↗

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↗

arXiv2015

A Hamiltonian Monte Carlo Method for Non-Smooth Energy Sampling

Efficient sampling from high-dimensional distributions is a challenging issue which is encountered in many large data recovery problems involving Markov chain Monte Carlo schemes. In this context, sampling using Hamiltonian dynamics is one of the recent techniques that have been proposed to exploit the target distribution geometry. Such schemes have clearly been shown to be efficient for multi-dimensional sampling, but are rather adapted to the exponential families of distributions with smooth energy function. In this paper, we address the problem of using Hamiltonian dynamics to sample from probability distributions having non-differentiable energy functions such as $\ell_1$. Such distributions are being more and more used in sparse signal and image recovery applications. The proposed technique uses a modified leapfrog transform involving a proximal step. The resulting non-smooth Hamiltonian Monte Carlo (ns-HMC) method is tested and validated on a number of experiments. Results show its ability to accurately sample according to various multivariate target distributions. The proposed technique is illustrated on synthetic examples and is applied to an image denoising problem.

stat.ME↗