Texture analysis can be conducted within the mathematical framework of multifractal analysis (MFA) via the study of the regularity fluctuations of image amplitudes. Successfully used in various applications, however MFA remains limited to the independent analysis of single images while, in an increasing number of applications, data are multi-temporal. The present contribution addresses this limitation and introduces a Bayesian framework that enables the joint estimation of multifractal parameters for multi-temporal images. It builds on a recently proposed Gaussian model for wavelet leaders parameterized by the multifractal attributes of interest. A joint Bayesian model is formulated by assigning a Gaussian prior to the second derivatives of time evolution of the multifractal attributes associated with multi-temporal images. This Gaussian prior ensures that the multifractal parameters have a smooth temporal evolution. The associated Bayesian estimators are then approximated using a Hamiltonian Monte-Carlo algorithm. The benefits of the proposed procedure are illustrated on synthetic data.

This paper addresses the problem of designing efficient sampling moves in order to accelerate the convergence of MCMC methods. The Partially collapsed Gibbs sampler (PCGS) takes advantage of variable reordering, marginalization and trimming to accelerate the convergence of the traditional Gibbs sampler. This work studies two specific moves which allow the convergence of the PCGS to be further improved. It considers a Bayesian model where structured sparsity is enforced using a multivariate Bernoulli Laplacian prior. The posterior distribution associated with this model depends on mixed discrete and continuous random vectors. Due to the discrete part of the posterior, the conventional PCGS gets easily stuck around local maxima. Two Metropolis-Hastings moves based on multiple dipole random shifts and inter-chain proposals are proposed to overcome this problem. The resulting PCGS is applied to EEG source localization. Experiments conducted with synthetic data illustrate the effectiveness of this PCGS with accelerated convergence.

This communication introduces a new framework for incorporating spatial regularization into a nonlinear unmixing procedure dedicated to hyperspectral data. The proposed model promotes smooth spatial variations of the nonlinear component in the mixing model. The spatial regularizer and the nonlinear contributions are jointly modeled by a vector-valued function that lies in a reproducing kernel Hilbert space (RKHS). The unmixing problem is strictly convex and reduces to a quadratic programming (QP) problem. Simulations on synthetic data illustrate the effectiveness of the proposed approach.

As part of a satellite communications system, the characteristics of the communication links make it difficult to set up telecommunications systems. For certain applications and protocols (TCP for example), the main problem is the propagation delay which reaches 500 ms for the round trip of the signal via a geostationary satellite. Another problem is the loss of data due to the characteristics of the transmission channel. For these reasons, protocols that ensure the reliability of communications must be set up on a satellite link. The aim of this thesis is to propose a mechanism that ensures the reliability of communication and maximize the utilization efficiency of the available bandwidth. HARQ protocol (Hybrid Automatic Repeat reQuest) is known for its ability to achieve the best compromise reliability/throughput. However, this mechanism which is now used in most terrestrial standards, is not well adapted for a satellite link. First, we propose a reliability method based on static HARQ. This method is specifically for services that tolerate some delay before the reception of the message. It consists in defining the probability of decoding at each transmission, using an optimization algorithm that we propose. The number of bits to be sent is calculated based on these probabilities and the distribution of the mutual information, assuming knowledge of the statistical distribution of the channel attenuation. Secondly, we introduce an adaptive version of the proposed method. Unlike the method proposed previously, this new approach calculates the number of bits to be sent by taking into account variations of the channel state during the communication. In fact, instead of sending a fixed number of bits at each transmission, the receiver calculates the number of bits to be sent depending on the channel state during the current transmission. Finally, we propose a frame structure for a physical layer that implements the proposed mechanisms and evaluate their performance by varying the system parameters. The aim is to find the optimal order of frame sizes and codes to be used and also to define the best strategy of transmission to be adopted by the transmitter.

As part of a satellite communications system, the characteristics of the communication links make it difficult to set up telecommunications systems. For certain applications and protocols (TCP for example), the main problem is the propagation delay which reaches 500 ms for the round trip of the signal via a geostationary satellite. Another problem is the loss of data due to the characteristics of the transmission channel. For these reasons, protocols that ensure the reliability of communications must be set up on a satellite link. The aim of this thesis is to propose a mechanism that ensures the reliability of communication and maximize the utilization efficiency of the available bandwidth. HARQ protocol (Hybrid Automatic Repeat reQuest) is known for its ability to achieve the best compromise reliability/throughput. However, this mechanism which is now used in most terrestrial standards, is not well adapted for a satellite link. First, we propose a reliability method based on static HARQ. This method is specifically for services that tolerate some delay before the reception of the message. It consists in defining the probability of decoding at each transmission, using an optimization algorithm that we propose. The number of bits to be sent is calculated based on these probabilities and the distribution of the mutual information, assuming knowledge of the statistical distribution of the channel attenuation. Secondly, we introduce an adaptive version of the proposed method. Unlike the method proposed previously, this new approach calculates the number of bits to be sent by taking into account variations of the channel state during the communication. In fact, instead of sending a fixed number of bits at each transmission, the receiver calculates the number of bits to be sent depending on the channel state during the current transmission. Finally, we propose a frame structure for a physical layer that implements the proposed mechanisms and evaluate their performance by varying the system parameters. The aim is to find the optimal order of frame sizes and codes to be used and also to define the best strategy of transmission to be adopted by the transmitter.

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 talk, we shall present 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.

De par leur complexité toujours plus croissante, les systèmes embarqués avioniques récents sont exposés à des menaces externes dont le potentiel de nuisance peut être préoccupant vis-à-vis des enjeux opérationnels. Auparavant restreints à un monde avionique bien délimité et très spécifique, on assiste de plus en en plus à une augmentation des capacités de connectivité de ces systèmes et à des possibilités d’intégration avec des technologies « monde ouvert », par exemple pour interagir avec des équipements passagers.

L'invention a pour objet un procédé d'identification d'émetteurs par un terminal dans un réseau iso-fréquence comprenant une pluralité d'émetteurs. Les émetteurs sont synchronisés et émettent avec un retard artificiel τ propre à chaque émetteur. Le procédé comporte au moins une étape (100) d'acquisition de la position approximative du terminal , de la position p d'une liste d'émetteurs {Tx} au voisinage du terminal et des retards des retard τ leurs étant associés, une étape (101) de mesures de pseudo-distances ρ entre les émetteurs et le terminal et une étape (102) d'association des mesures ρ aux émetteurs de positions connues p en minimisant une fonction de coût, ladite fonction de coût correspondant à la norme de l'erreur entre les mesures ρi et un modèle de mesures des pseudo-distances appliqué à une permutation de la position des émetteurs.

Depending on the congestion level and the network characteristics (e.g., buffer sizes, capacity of the bottleneck, deployment scenario, etc.) a fixed Initial Window (IW) would be either too conservative or too aggressive. This results in low usage of the network resource or damaging high congestion level. This paper presents a sender-side only modification to the slow-start of TCP, SmartIW, that bypasses the limitations and potential issues of a fixed IW. The Round Trip Time (RTT) is estimated during the establishment of the connection and further exploited by SmartIW to pace the transmission of an adequate number of packets during the first RTT. Our simulation results show that, since the IW has been set in adequacy with the available network information, larger IW can be transmitted without increasing the congestion level of the network. SmartIW eventually reduces the RTT dependence of the slow start stage to fairly provide significant performance improvements whatever the network characteristics (RTT and congestion level).

Multifractal (MF) analysis enables the theoretical study of scale invariance models and their practical assessment via wavelet leaders. Yet, the accurate estimation of MF parameters remains a challenging task. For a range of applications, notably biomedical, the performance can potentially be improved by taking advantage of the multivariate nature of data. However, this has barely been considered in the context of MF analysis. This paper proposes a Bayesian model that enables the joint estimation of MF parameters for multivariate time series. It builds on a recently introduced statistical model for leaders and is formulated using a 3D gamma Markov random field joint prior for the MF parameters of the voxels of spatio-temporal data, represented as a multivariate time series, that counteracts the statistical variability induced by small sample size. Numerical simulations indicate that the proposed Bayesian estimator significantly outperforms current state-of-the-art algorithms.