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.

The use of the continuous phase modulation (CPM) is interesting when the channel represents a strong non-linearity and in the case of limited spectral support ; particularly for the uplink, where the satellite holds an amplifier per carrier, and for downlinks where the terminal equipment works very close to the saturation region. Numerous studies have been conducted on this issue but the proposed solutions use iterative CPM demodulation/decoding concatenated with convolutional or block error correcting codes. The use of LDPC codes has not yet been introduced. Particularly, no works, to our knowledge, have been done on the optimization of sparse graph-based codes adapted for the context described here. In this study, we propose to perform the asymptotic analysis and the design of turbo-CPM systems based on the optimization of sparse graph-based codes. Moreover, an analysis on the corresponding receiver will be done.

The use of the continuous phase modulation (CPM) is interesting when the channel represents a strong non-linearity and in the case of limited spectral support; particularly for the uplink, where the satellite holds an amplifier per carrier, and for downlinks where the terminal equipment works very close to the saturation region. Numerous studies have been conducted on this issue but the proposed solutions use iterative CPM demodulation/decoding concatenated with convolutional or block error correcting codes. The use of LDPC codes has not yet been introduced. Particularly, no works, to our knowledge, have been done on the optimization of sparse graph-based codes adapted for the context described here. In this study, we propose to perform the asymptotic analysis and the design of turbo-CPM systems based on the optimization of sparse graph-based codes. Moreover, an analysis on the corresponding receiver will be done.

In this thesis, we look at the possibility to deploy a Lower-than-Best-Effort (LBE) service over long delay links such as satellite links. The objective is to provide a second priority class dedicated to background or signaling traffic. In the context of long delay links, an LBE service might also help to optimize the use of the link capacity. In addition, an LBE service can enable a low-cost or even free Internet access to remote communities via satellite communication. Two possible deployment levels of an LBE approach exists : either at the MAC layer or at the transport layer. In this thesis, we are interested in an end-to-end approach and thus specifically focus on transport layer solutions. We first propose to study LEDBAT (Low Extra Delay Background Transport) because of its potential. Indeed, LEDBAT has been standardized by the IETF and is widely deployed within the official BitTorrent client. Unfortunately, the tuning of LEDBAT parameters is revealed to highly depend on network conditions. In the worst case scenario, LEDBAT flows can starve other traffic such as commercial traffic performing over a satellite link. LEDBAT also suffers from an intra-unfairness issue, called the latecomer advantage. These reasons often prevent operators from using LBE protocols over wireless and long-delay links as a misconfiguration can overload link capacity. Therefore, we design FLOWER, a new delay-based transport protocol, as an alternative to LEDBAT. By using a fuzzy controller to modulate the sending rate, FLOWER aims to solve LEDBAT issues while fulfilling the role of an LBE protocol. Our simulation results show that FLOWER can carry LBE traffic not only in the long delay context, but in a wide range of network conditions where LEDBAT usually fails.

In this thesis, we look at the possibility to deploy a Lower-than-Best-Effort (LBE) service over long delay links such as satellite links. The objective is to provide a second priority class dedicated to background or signaling traffic. In the context of long delay links, an LBE service might also help to optimize the use of the link capacity. In addition, an LBE service can enable a low-cost or even free Internet access to remote communities via satellite communication. Two possible deployment levels of an LBE approach exists : either at the MAC layer or at the transport layer. In this thesis, we are interested in an end-to-end approach and thus specifically focus on transport layer solutions. We first propose to study LEDBAT (Low Extra Delay Background Transport) because of its potential. Indeed, LEDBAT has been standardized by the IETF and is widely deployed within the official BitTorrent client. Unfortunately, the tuning of LEDBAT parameters is revealed to highly depend on network conditions. In the worst case scenario, LEDBAT flows can starve other traffic such as commercial traffic performing over a satellite link. LEDBAT also suffers from an intra-unfairness issue, called the latecomer advantage. These reasons often prevent operators from using LBE protocols over wireless and long-delay links as a misconfiguration can overload link capacity. Therefore, we design FLOWER, a new delay-based transport protocol, as an alternative to LEDBAT. By using a fuzzy controller to modulate the sending rate, FLOWER aims to solve LEDBAT issues while fulfilling the role of an LBE protocol. Our simulation results show that FLOWER can carry LBE traffic not only in the long delay context, but in a wide range of network conditions where LEDBAT usually fails.

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 consider 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 benefit from both 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 through simulations conducted on both synthetic and real data.

Paraxial approximation defines the electric field of an optical beam at each point as a two-dimensional vector orthogonal to the direction of propagation. The Stokes decomposition theorem asserts that “any light beam is equivalent to the sum of two lights, one of which is polarized and the other unpolarized”. In a modern framework of random stationary processes, the theorem needs more accurate statements. In this paper, we study three-dimensional fields, and we prove that the decomposition problem has at most two solutions (except for an undetermined argument) which are characterized by well determined circuits of LIF (Linear Invariant Filters).

Transmission count, the number of transmissions required for delivering a data packet over a link, is part of almost all state-of-the-art routing metrics for wireless networks. In traditional networks, peer-to-peer interference and channel errors are what define its value for the most part. In cognitive radio networks, however, there is a third culprit that can impact the transmission count: primary user interference. It may be tempting to think of primary user interference as no different than interference caused by other peers. However, unlike peers, primary users do not follow the same protocol and have strict channel access priority over the secondary users. Motivated by this observation, we carry out an empirical study on a USRP testbed for analyzing the impact of primary users. Our measurements show that a primary user has a distinct impact on the transmission count, which the de facto standard approach, ETX, designed for traditional networks, fails to capture. To resolve this, we present COExiST (for COgnitive radio EXpected transmISsion counT): a link metric that accurately captures the expected transmission count over a wireless link subject to primary user interference. Extensive experiments on a five-node USRP testbed demonstrate that COExiST accurately captures the actual transmission count in the presence of primary users – the 80th percentile of the error is less than 20%.