The decomposition of an optical beam in a polarized part added to an unpolarized part was studied by G.G. Stokes among numerous other works. Today, the problem is no longer a trigonometric manipulation proper to monochromatic waves, but a problem handling stationary processes with band spectra. In literature, the question seems to be: given some spectral properties and some propagation medium, can we obtain a decomposition? Furthermore, in the case of a positive answer, we have to provide devices for exhibiting solutions. In a linear framework, the problem always has a solution (and even an infinity) whatever the chosen polarization direction. In this paper, we study the links which appear most often between the members of the decomposition.

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.

While Transmission Control Protocol (TCP) Performance Enhancing Proxy (PEP) solutions have long been undisputed to solve the inherent satellite problems, the improvement of the regular end-to-end TCP congestion avoidance algorithms and the recent emphasis on the PEPs drawbacks have opened the question of the PEPs sustainability. Nevertheless, with a vast majority of Internet connections shorter than ten segments, TCP PEPs continue to be required to counter the poor efficiency of the end-to-end TCP start-up mechanisms. To reduce the PEPs dependency, designing a new fast start-up TCP mechanism is therefore a major concern. But, while enlarging the Initial Window (IW) up to ten segments is, without any doubt, the fastest solution to deal with a short-lived connection in an uncongested network, numerous researchers are concerned about the impact of the large initial burst on an already congested network. Based on traffic observations and real experiments, Initial Spreading has been designed to remove those concerns whatever the load and type of networks. It offers performance similar to a large IW in uncongested network and outperforms existing end-to-end solutions in congested networks. In this paper, we show that Initial Spreading, taking care of the satellite specificities, is an efficient end-to-end alternative to the TCP PEPs.

In urban canyons, non-line-of-sight (NLOS) multipath interferences affect position estimation based on global navigation satellite systems (GNSS). This paper proposes to model the effects of NLOS multipath interferences as mean value jumps contaminating the GNSS pseudo-range measurements. The marginalized likelihood ratio test (MLRT) is then investigated to detect, identify and estimate the corresponding NLOS multipath biases. However, the MLRT test statistics is difficult to compute. In this work, we consider a Monte Carlo integration technique based on bias magnitude sampling. Jensen's inequality allows this Monte Carlo integration to be simplified. The multiple model algorithm is also used to update the prior information for each bias magnitude sample. Some strategies are designed for estimating and correcting the NLOS multipath biases. In order to demonstrate the performance of the MLRT, experiments allowing several localization methods to be compared are performed. Finally, results from a measurement campaign conducted in an urban canyon are presented in order to evaluate the performance of the proposed algorithm in a representative environment.

The theory of uniform sampling, developed among others by C. Shannon, is the foundation of today digital signal processing. Since then, numerous works have been dedicated to non uniform sampling schemes. On the one hand, these schemes model uniform sampling device imperfections. On the other hand, sampling can be intentionally performed in a non uniform way to benefit from specific properties, in particular simplifications concerning the choice of the mean sampling frequency. Most of these works have focused on theoretical approaches, adopting simplified models for signals and sampling devices. However, in many application domains, such as satellite communications, analog-to-digital conversion is submitted to strong constraints over the involved bandwidth due to the very high frequencies used. These operational conditions enhance the imperfections of the involved electronic devices and require the choice of particular signal models and sampling schemes. This thesis aims at proposing sampling models suitable for this context. These models apply to random band-pass signals, which are the classical models for telecommunication signals. They must take into account technological, economical factors and on-board complexity constraints and allow to integrate particular functionalities useful for telecommunication applications. This thesis first contribution is to develop non uniform sampling formulas that can digitally integrate functionalities that appear to be tricky in the analog domain at the considered frequencies. The thesis second contribution consists in applying non uniform sampling theory to the estimation and compensation of synchronization errors encountered in particular sampling devices, the time-interleaved analog-to-digital converters. This estimation will be performed through supervised or blind methods.

The theory of uniform sampling, developed among others by C. Shannon, is the foundation of today digital signal processing. Since then, numerous works have been dedicated to non uniform sampling schemes. On the one hand, these schemes model uniform sampling device imperfections. On the other hand, sampling can be intentionally performed in a non uniform way to benefit from specific properties, in particular simplifications concerning the choice of the mean sampling frequency. Most of these works have focused on theoretical approaches, adopting simplified models for signals and sampling devices. However, in many application domains, such as satellite communications, analog-to-digital conversion is submitted to strong constraints over the involved bandwidth due to the very high frequencies used. These operational conditions enhance the imperfections of the involved electronic devices and require the choice of particular signal models and sampling schemes. This thesis aims at proposing sampling models suitable for this context. These models apply to random band-pass signals, which are the classical models for telecommunication signals. They must take into account technological, economical factors and on-board complexity constraints and allow to integrate particular functionalities useful for telecommunication applications. This thesis first contribution is to develop non uniform sampling formulas that can digitally integrate functionalities that appear to be tricky in the analog domain at the considered frequencies. The thesis second contribution consists in applying non uniform sampling theory to the estimation and compensation of synchronization errors encountered in particular sampling devices, the time-interleaved analog-to-digital converters. This estimation will be performed through supervised or blind methods.

Random propagation times are able to model waves attenuation and velocity. It is true for electromagnetic waves (light, radar, guided propagation) and also for acoustics and ultrasounds (acoustics for high frequencies). About the latter, it can be shown that stable probability laws are well-fitted for frequencies up to dozens of megahertz in numerous cases. Nowadays, medical applications are performed using propagation through perfluorocarbon (PFC). Experiments were done to measure attenuations and phase changes. Using these results, this paper addresses the question to know if stable probability laws can be used to characterize the propagation of ultrasounds through PFC liquids.

This paper studies a fast multi-band image fusion algorithm for highspatial low-spectral resolution and low-spatial high-spectral resolution images. The popular forward model and the conventional Gaussian prior are used to form the posterior of the target image. Maximizing the posterior leads to solving a matrix Sylvester equation. By exploiting the properties of the circulant and decimation matrices associated with the fusion problem, a closed-form solution for the corresponding Sylvester equation is obtained, avoiding any iterative update step. 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.

We develop a novel high-resolution method for the estimation of the direction of incidence of energy emitted by sources in 3D space from wideband measurements collected by a planar array of sensors. We make use of recent generalizations of Kronecker’s theorem and formulate the direction of arrival estimation problem as an optimization problem in the space of sequences generating so called “general domain Hankel matrices” of fixed rank. The unequal sampling at different wavelengths is handled by using appropriate interpolation operators. The algorithm is operational for general array geometries (i.e., not restricted to, e.g., rectangular arrays) and for equidistantly as well as unequally spaced receivers. Numerical simulations for different sensor arrays and various signal-to-noise ratios are provided and demonstrate its excellent performance.

In this paper, we propose a hierarchical Bayesian model approximating the l20 mixed-norm regularization by a multivariate Bernoulli Laplace prior to solve the EEG inverse problem by promoting spatial structured sparsity. The posterior distribution of this model is too complex to derive closed-form expressions of the standard Bayesian estimators. However, this posterior can be sampled using an MCMC method and the generated samples can be used to compute Bayesian estimators of the unknown model parameters. The proposed MCMC algorithm is based on a partially collapsed Gibbs sampler and a dual dipole random shift proposal for the non-zero positions. Note that the proposed method estimates the brain activity and all other model parameters jointly in a completely unsupervised framework. The results obtained on synthetic data with controlled ground truth show the good performance of the proposed method when compared to the l21 approach in different scenarios, and its capacity to estimate point-like source activity.