Sparse signal/image recovery is a challenging topic that has captured a great interest during the last decades, especially in the biomedical field. Many techniques generally try to regularize the considered ill-posed inverse problem by defining appropriate priors for the target signal/image. The target regularization problem can then be solved either in a variational or Bayesian context. However, a little interest has been devoted to the uncertainties about the linear operator, which can drastically alter the reconstruction quality. In this paper, we propose a novel method for signal/image recovery that accounts and corrects the linear operator imprecisions. The proposed approach relies on a Bayesian formulation which is applied to EEG signal recovery. Our results show the promising potential of the proposed method compared to other regularization techniques which do not account for any error affecting the linear operator.

This letter 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.

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 multiscattering 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 article, we present an overview of recent advances in nonlinear unmixing modeling.

Cospas-Sarsat is an international search and rescue system that operates using low-orbit satellites and geostationary satellites. The current satellite constellation is being replaced by medium Earth orbit satellites which will cover larger areas of the surface of the Earth, permitting almost instantaneous alerts. The objective of this thesis is to study the localization performance of this new system, named MEOSAR (Medium Earth Orbit Search and Rescue). We first study the quality of the link between the beacon, the satellite and the ground receiving station through a link budget. Then, we propose a signal model based on sigmoidal functions to model the smooth transitions of the distress signal. For this model, the localization performance (in terms of Cramér-Rao bounds and estimator variances) is studied for the estimation of the beacon position and for different parameters including the time of arrival, the frequency of arrival and the symbol width. Then, we study the impact of adding prior information on the symbol width and the signal rise time, which are constructed from the allowed tolerances on the beacon specifications. We also investigate the error introduced by the addition of oscillator phase noise, and we show how the position estimation can be improved by taking into account multiple emissions of the beacon. Finally, the localization performance of the MEOSAR system is studied for second generation beacons, which are being developed using spread spectrum modulation.

Cospas-Sarsat is an international search and rescue system that operates using low-orbit satellites and geostationary satellites. The current satellite constellation is being replaced by medium Earth orbit satellites which will cover larger areas of the surface of the Earth, permitting almost instantaneous alerts. The objective of this thesis is to study the localization performance of this new system, named MEOSAR (Medium Earth Orbit Search and Rescue). We first study the quality of the link between the beacon, the satellite and the ground receiving station through a link budget. Then, we propose a signal model based on sigmoidal functions to model the smooth transitions of the distress signal. For this model, the localization performance (in terms of Cramér-Rao bounds and estimator variances) is studied for the estimation of the beacon position and for different parameters including the time of arrival, the frequency of arrival and the symbol width. Then, we study the impact of adding prior information on the symbol width and the signal rise time, which are constructed from the allowed tolerances on the beacon specifications. We also investigate the error introduced by the addition of oscillator phase noise, and we show how the position estimation can be improved by taking into account multiple emissions of the beacon. Finally, the localization performance of the MEOSAR system is studied for second generation beacons, which are being developed using spread spectrum modulation.

In this paper, we evaluate several multiuser detection (MUD) architectures for the reception of asynchronous beacon signals in the ARGOS satellite system. The case of synchronous signals is studied first. Though impractical, this case provides useful guidance on the second part of the study, that is, the design of MUD receivers for asynchronous users. This paper focuses more particularly on successive interference cancellation (SIC) receivers because they have been shown to achieve a good performance complexity trade-off. Several Eb ∕ N0 degradation curves are obtained as a function of channel parameters. With these curves, a performance analysis is presented in order to determine in which conditions it is possible to successfully decode none, one, or more beacon signals. We show that SIC receivers can improve the percentage of served beacons from 50% to more than 67% for a population of 37,600 beacons.

Satellite navigation signals demodulation performance is historically tested and compared in the Additive White Gaussian Noise propagation channel model which well simulates the signal reception in open areas. Nowadays, the majority of new applications targets dynamic users in urban environments; therefore the implementation of a simulation tool able to provide realistic GNSS signal demodulation performance in obstructed propagation channels has become mandatory. This paper presents the simulator SiGMeP (Simulator for GNSS Message Performance), which is wanted to provide demodulation performance of any GNSS signals in urban environment, as faithfully of reality as possible. The demodulation performance of GPS L1C simulated with SiGMeP in the AWGN propagation channel model, in the Prieto propagation channel model (narrowband Land Mobile Satellite model in urban configuration) and in the DLR channel model (wideband Land Mobile Satellite model in urban configuration) are computed and compared one to the other. The demodulation performance for both LMS channel models is calculated using a new methodology better adapted to urban environments, and the impact of the received signal phase estimation residual errors has been taken into account (ideal estimation is compared with PLL tracking). Finally, a refined figure of merit used to represent GNSS signals demodulation performance in urban environment is proposed.

Due to its heavy-tailed and fully parametric form, the multivariate generalized Gaussian distribution (MGGD) has been receiving much attention in signal and image processing applications. Considering the estimation issue of the MGGD parameters, the main contribution of this paper is to prove that the maximum likelihood estimator (MLE) of the scatter matrix exists and is unique up to a scalar factor, for a given shape parameter. Moreover, an estimation algorithm based on a Newton-Raphson recursion is proposed for computing the MLE of MGGD parameters. Various experiments conducted on synthetic and real data are presented to illustrate the theoretical derivations in terms of number of iterations and number of samples for different values of the shape parameter. The main conclusion of this work is that the parameters ofMGGDs can be estimated using the maximum likelihood principle with good performance.

We investigate the design of a broadcast system in order to maximize throughput. This task is usually challenging due to channel variability. Forty years ago, Cover introduced and compared two schemes: time sharing and superposition coding. Even if the second scheme was proved to be optimal for some channels, modern satellite communications systems such as DVB-SH and DVB-S2 rely mainly on a time sharing strategy to optimize the throughput. They consider hierarchical modulation, a practical implementation of superposition coding, but only for unequal error protection or backward compatibility purposes. In this article, we propose to combine time sharing and hierarchical modulation together and show how this scheme can improve the performance in terms of available rate. We introduce a hierarchical 16-APSK to boost the performance of the DVB-S2 standard. We also evaluate various strategies to group the receivers in pairs when using hierarchical modulation. Finally, we show in a realistic case, based on DVB-S2, that the combined scheme can provide throughput gains greater than 10% compared to the best time sharing strategy.

This thesis aims to introduce multifrequency phase tracking algorithms operating in low C/N0 environment. The objective is to develop new structures whose tracking limits are lower than that of current algorithms used in mass market receivers. Phase tracking suffers from a lack of robustness due to the cycle slip phenomenon. Works have thus been focused on elaborating new phase unwrapping systems. To do so, two different tracking approaches were studied. First, we have developed new monofrequency tracking loops based on a conventional DPLL. These structures aim at predicting the discriminator output by analyzing, thanks to a polynomial model, the last output samples of either the discriminator or the loop filter. Once the discriminator output is predicted, the estimated value is pre-compensated so that the phase dynamics to be tracked is reduced as well as the cycle slip rate. Then, the unwrapping structure analyzing the loop filter outputs has been extended to multifrequency signals. Using a data fusion step, the new multifrequency structure takes advantage of the frequency diversity of a GNSS signal (i.e., proportionality of Doppler frequencies) to improve the tracking performances. Secondly, studies have been focused on developing a new multifrequency tracking algorithm using variational Bayesian filtering technique. This tracking method, which also uses the GNSS frequency diversity, assumes a Markovian phase dynamics that enforces the smoothness of the phase estimation and unwraps it.