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.

The specifications of Digital Video Broadcasting - Return Channel via Satellite (DVB-RCS2) state that the satellite gateway could introduce both random and dedicated access methods to distribute the capacity among the different home users. Before starting an engineering process to design an algorithm allowing to combine both methods, it seems necessary to assess the performance of each. This paper compares random and dedicated access methods by measuring their impact on the performance of Transmission Control Protocol (TCP) sessions when the home users exploit the DVB-RCS2 link for regular use (e.g., web browsing or email transmission). In this paper we detail the implementation of an NS-2 module emulating Physical Channel Access (PCA). This module fills a gap in terms of random and deterministic access methods and allows to model various satellite channel access strategies. Based on NS-2 simulations using realistic system parameters of the DVB-RCS2 link, we demonstrate that, compared to dedicated access methods, which generally result in higher levels of transmitted data, random access methods enable faster transmission for short flows. We propose to combine random and dedicated access methods, with the selection of a specific method dependent on the dynamic load of the network and the sequence number of the TCP segments.

This paper presents a Bayesian fusion technique for remotely sensed multi-band images. The observed images are related to the high spectral and high spatial resolution image to be recovered through physical degradations, e.g., spatial and spectral blurring and/or subsampling defined by the sensor characteristics. The fusion problem is formulated within a Bayesian estimation framework. An appropriate prior distribution exploiting geometrical considerations is introduced. To compute the Bayesian estimator of the scene of interest from its posterior distribution, a Markov chain Monte Carlo algorithm is designed to generate samples asymptotically distributed according to the target distribution. To efficiently sample from this high-dimension distribution, a Hamiltonian Monte Carlo step is introduced within a Gibbs sampling strategy. The efficiency of the proposed fusion method is evaluated with respect to several state-of-the-art fusion techniques.

AStrion is an automatic spectrum analyser software, which proposes a new generic and data-driven method without any a priori information on the measured signals. In order to compute some general characteristics and derive the properties of the signal, the first step in this approach is to give some insight into the nature of the signal. This pre-analysis, the so-called data validation, contains a number of tests to reveal some of the properties and characteristics of the data, such as the acquisition validity (the absence of saturation and a posteriori in respect of the sampling theorem), the stationarity (or non-stationarity), the periodicity and the signal-to-noise ratio. Based on these characteristics, the proposed method defines indicators and alarm trigger thresholds and also categorises the signal into three classes, which helps to guide the following spectral analysis. The present paper introduces the four tests of this pre-analysis and the signal categorisation rules. Finally, the proposed approach is validated on a set of wind turbine vibration measurements to demonstrate its applicability for a long-term and continuous monitoring of real-world signals.