This paper proposes a new method for data reception over a random access channel in a satellite communication system. The method is called Multi-replicA decoding using corRelation baSed locALisAtion (MARSALA). It uses the same transmission scheme as in Contention Resolution Diversity Slotted Aloha (CRDSA) where each user sends several replicas of the same packet over the frame. MARSALA is a new decoding technique that localises all the replicas of a packet using a correlation based method, then combines them to decode the data. With MARSALA, the system can achieve a normalized throughput higher than 1.2, resulting in a significant gain compared to CRDSA, while adding a relatively low implementation complexity at the receiver. We also highlight on the practical issues related to channel estimation and how to perform coherent signal combination in MARSALA.

Cet article traite du problème de l'échantillonnage non uniforme dans le cas des processus aléatoires. Une nouvelle méthode est proposée permettant d'effectuer une reconstruction exacte du signal avec une meilleure vitesse de convergence en termes de nombre d'échantillons et un filtrage linéaire directement à partir des échantillons non uniformes. Ce procédé peut être appliqué à des signaux de type passe-bas comme à des signaux de type passe-bande.

This paper proposes a hierarchical Bayesian model for estimating the parameters of asymmetric power distributions (APDs). These distributions are defined by shape, scale and asymmetry parameters which make them very flexible for approximating empirical distributions. A hybrid Markov chain Monte Carlo method is then studied to sample the unknown parameters of APDs. The generated samples can be used to compute the Bayesian estimators of the unknown APD parameters. Numerical experiments show the good performance of the proposed estimation method. An application to an image segmentation problem is finally investigated.

Bayesian sparse signal recovery has been widely investigated during the last decade due to its ability to automatically estimate regularization parameters. Prior based on mixtures of Bernoulli and continuous distributions have recently been used in a number of recent works to model the target signals, often leading to complicated posteriors. Inference is therefore usually performed using Markov chain Monte Carlo algorithms. In this paper, a Bernoulli-generalized Gaussian distribution is used in a sparse Bayesian regularization framework to promote a two-level flexible sparsity. Since the resulting conditional posterior has a non-differentiable energy function, the inference is conducted using the recently proposed non-smooth Hamiltonian Monte Carlo algorithm. Promising results obtained with synthetic data show the efficiency of the proposed regularization scheme.

This paper proposes an unsupervised Bayesian algorithm for unmixing successive hyperspectral images while accounting for temporal and spatial variability of the endmembers. Each image pixel is modeled as a linear combination of the endmembers weighted by their corresponding abundances. Spatial endmember variability is introduced by considering the normal compositional model that assumes variable endmembers for each image pixel. A prior enforcing a smooth temporal variation of both endmembers and abundances is considered. The proposed algorithm estimates the mean vectors and covariance matrices of the endmembers and the abundances associated with each image. Since the estimators are difficult to express in closed form, we propose to sample according to the posterior distribution of interest and use the generated samples to build estimators. The performance of the proposed Bayesian model and the corresponding estimation algorithm is evaluated by comparison with other unmixing algorithms on synthetic images.

Hyperspectral unmixing aims at determining the reference spectral signatures composing a hyperspectral image, their abundance fractions and their number. In practice, the spectral variability of the identified signatures induces significant abundance estimation errors. To address this issue, this paper introduces a new linear mixing model explicitly accounting for this phenomenon. In this setting, the extracted endmembers are interpreted as possibly corrupted versions of the true endmembers. 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.

Texture analysis is central in many image processing problems. It can be conducted by studying the local regularity fluctuations of image amplitudes, and multifractal analysis provides a theoretical and practical framework for such a characterization. Yet, due to the non Gaussian nature and intricate dependence structure of multifractal models, accurate parameter estimation is challenging : standard estimators yield modest performance, and alternative (semi-)parametric estimators exhibit prohibitive computational cost for large images. This present contribution addresses these difficulties and proposes a Bayesian procedure for the estimation of the multifractality parameter c2 for images. It relies on a recently proposed semi-parametric model for the multivariate statistics of log-wavelet leaders and on a Whittle approximation that enables its numerical evaluation. The key result is a closed-form expression for the Whittle likelihood. Numerical simulations indicate the excellent performance of the method, significantly improving estimation performance over standard estimators and computational efficiency over previously proposed Bayesian estimators.

The profusion of spectral bands generated by the acquisition process of hyperspectral images generally leads to high computational costs. Such difficulties arise in particular with nonlinear unmixing methods, which are naturally more complex than linear ones. This complexity, associated with the high redundancy of information within the complete set of bands, make the search of band selection algorithms relevant. With this work, we propose a band selection strategy in reproducing kernel Hilbert spaces that allows to drastically reduce the processing time required by nonlinear unmixing techniques. Simulation results show a complexity reduction of two orders of magnitude without compromising unmixing performance.

Electrical engineering teaching is not an easy task because of the broad spectrum of knowledge to call for (electromagnetic, electronic, control, signal processing), each one having its specific formalism. To connect these different courses through a real-life application, we have decided to design a fire-control model based on a low-cost sonar system. This experiment has been designed for graduated students and is exploited in laboratory projects. Besides the playful aspects brought by the model, the project allows to face-off a real system and requires strong initiative from the students to success.