Central Limit Theorems for Wavelet Packet Decompositions of Stationary Random Processes

This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of any given path of the $M$-band wavelet packet decomposition tree. It is shown that if the input process is centred and strictly stationary, these sequences converge in distribution to white Gaussian processes when the resolution level increases, provided that the decomposition filters satisfy a suitable property of regularity. For any given path, the variance of the limit white Gaussian process directly relates to the value of the input process power spectral density at a specific frequency.Comment: Submitted to the IEEE Transactions on Signal Processing, October 200

Statistical approach for human electromagnetic exposure assessment in future wireless ATTO-cell networks

In this article, we study human electromagnetic exposure to the radiation of an ultra dense network of nodes integrated in a floor denoted as ATTO-cell floor, or ATTO-floor. ATTO-cells are a prospective 5 G wireless networking technology, in which humans are exposed by several interfering sources. To numerically estimate this exposure we propose a statistical approach based on a set of finite difference time domain simulations. It accounts for variations of antenna phases and makes use of a large number of exposure evaluations, based on a relatively low number of required simulations. The exposure was expressed in peak-spatial 10-g SAR average (psSAR(10g)). The results show an average exposure level of similar to 4.9 mW/kg and reaching 7.6 mW/kg in 5% of cases. The maximum psSAR(10g) value found in the studied numerical setup equals around 21.2 mW/kg. Influence of the simulated ATTO-floor size on the resulting exposure was examined. All obtained exposure levels are far below 4 W/kg ICNIRP basic restriction for general public in limbs (and 20 W/kg basic restriction for occupational exposure), which makes ATTO-floor a potential low-exposure 5 G candidate

Analyse des Séquences de Processus et Champs Aléatoires d'Ondelettes

Cette synthèse de travaux de recherche porte sur l'étude des processus aléatoires non-stationnaires lorsque ceux-ci sont projetés sur les bases fonctionnelles d'ondelettes. Dans les références citées, une analyse fine de tous les facteurs contribuant à la stationnarité et à la décorrélation des coefficients de projection est proposée, en fonction des structures de dépendances statistiques inhérentes au processus considéré. Cette analyse met en évidence 2 issues pour une même décomposition en ondelettes : certaines fonctions de la base d'ondelettes ont pour effet de casser les dépendances statistiques intrinsèques au processus décomposé tandis que d'autres fonctions concentrent ces dépendances dans des sous-espaces d'ondelettes spécifiques. En pratique, l'identification des sous espaces d'ondelettes associés à ces 2 issues permet de simplifier la sélection de modèles de descriptions statistiques et/ou probabilistes du processus analysé. On déduit ainsi que de nombreux champs stochastiques `textures' présents dans les images numériques peuvent être décrits de manière parcimonieuse par le biais de modèles paramétriques associés à leurs séquences de coefficients d'ondelettes. Ces descriptions sont utilisées dans les références citées pour proposer des méthodes de classification de textures, de recherche de contenu spécifique dans une base d'images et de détection de changements dans les séries temporelles d'images

Wavelet Packets of fractional Brownian motion: Asymptotic Analysis and Spectrum Estimation

International audienceThis work provides asymptotic properties of the autocorrelation functions of the wavelet packet coefficients of a fractional Brownian motion. It also discusses the convergence speed to the limit autocorrelation function, when the input random process is either a fractional Brownian motion or a wide-sense stationary second-order random process. The analysis concerns some families of wavelet paraunitary filters that converge almost everywhere to the Shannon paraunitary filters. From this analysis, we derive wavelet packet based spectrum estimation for fractional Brownian motions and wide-sense stationary random processes. Experimental tests show good results for estimating the spectrum of 1/f processes

Smooth Adaptation by Sigmoid Shrinkage

International audienceThis work addresses the properties of a sub-class of sigmoid based shrinkage functions: the non zero-forcing smooth sigmoid based shrinkage functions or SigShrink functions. It provides a SURE optimization for the parameters of the SigShrink functions. The optimization is performed on an unbiased estimation risk obtained by using the functions of this sub-class. The SURE SigShrink performance measurements are compared to those of the SURELET (SURE linear expansion of thresholds) parameterization. It is shown that the SURE SigShrink performs well in comparison to the SURELET parameterization. The relevance of SigShrink is the physical meaning and the flexibility of its parameters. The SigShrink functions perform weak attenuation of data with large amplitudes and stronger attenuation of data with small amplitudes, the shrinkage process introducing little variability among data with close amplitudes. In the wavelet domain, SigShrink is particularly suitable for reducing noise without impacting significantly the signal to recover. A remarkable property for this class of sigmoid based functions is the invertibility of its elements. This property makes it possible to smoothly tune contrast (enhancement - reduction)

Best Basis for Joint Representation: the Median of Marginal Best Bases for Low Cost Information Exchanges in Distributed Signal Representation

International audienceThe paper addresses the selection of the best representations for distributed and/or dependent signals. Given an indexed tree structured library of bases and a semi-collaborative distribution scheme associated with minimum information exchange (emission and reception of one single index corresponding to a marginal best basis), the paper proposes the median basis computed on a set of best marginal bases for joint representation or fusion of distributed/dependent signals. The paper provides algorithms for computing this median basis with respect to standard tree structured libraries of bases such as wavelet packet bases or cosine trees. These algorithms are effective when an additive information cost is under consideration. Experimental results performed on distributed signal compression confirms worthwhile properties for the median of marginal best bases with respect to the ideal best joint basis, the latter being underdetermined in practice, except when a full collaboration scheme is under consideration

Stochasticity: A Feature for the Structuring of Large and Heterogeneous Image Databases

International audienceThe paper addresses image feature characterization and the structuring of large and heterogeneous image databases through the stochasticity or randomness appearance. Measuring stochasticity involves finding suitable representations that can significantly reduce statistical dependencies of any order. Wavelet packet representations provide such a framework for a large class of stochastic processes through an appropriate dictionary of parametric models. From this dictionary and the Kolmogorov stochasticity index, the paper proposes semantic stochasticity templates upon wavelet packet sub-bands in order to provide high level classification and content-based image retrieval. The approach is shown to be relevant for texture images

Detection threshold for non-parametric estimation

International audienceA new threshold is presented for better estimating a signal by sparse transform and soft thresholding. This threshold derives from a non-parametric statistical approach dedicated to the detection of a signal with unknown distribution and unknown probability of presence in independent and additive white Gaussian noise. This threshold is called the detection threshold and is particularly appropriate for selecting the few observations, provided by the sparse transform, whose amplitudes are sufficiently large to consider that they contain information about the signal. An upper bound for the risk of the soft thresholding estimation is computed when the detection threshold is used. For a wide class of signals, it is shown that, when the number of observations is large, this upper bound is from about twice to four times smaller than the standard upper bounds given for the universal and the minimax thresholds. Many real-world signals belong to this class, as illustrated by several experimental results

Routing protocols and quality of services for security based applications using wireless video sensor networks

Wireless video sensor networks have been a hot topic in recent years; the monitoring capability is the central feature of the services offered by a wireless video sensor network can be classified into three major categories: monitoring, alerting, and information on-demand. These features have been applied to a large number of applications related to the environment (agriculture, water, forest and fire detection), military, buildings, health (elderly people and home monitoring), disaster relief, area and industrial monitoring. Security applications oriented toward critical infrastructures and disaster relief are very important applications that many countries have identified as critical in the near future. This paper aims to design a cross layer based protocol to provide the required quality of services for security related applications using wireless video sensor networks. Energy saving, delay and reliability for the delivered data are crucial in the proposed application. Simulation results show that the proposed cross layer based protocol offers a good performance in term of providing the required quality of services for the proposed application

Attosecond resolved charging of clusters

Attosecond laser pulses open the door to resolve microscopic electron dynamics in time. Experiments performed include the decay of a core hole, the time-resolved measurement of photo ionization and electron tunneling. The processes investigated share the coherent character of the dynamics involving very few, ideally one active electron. Here, we introduce a scheme to probe dissipative multi-electron motion in time. In this context attosecond probing enables one to obtain information which is lost at later times and cannot be retrieved by conventional methods in the energy domain due to the incoherent nature of the dynamics. As a specific example we will discuss the charging of a rare-gas cluster during a strong femtosecond pulse with attosecond pulses. The example illustrates the proposed use of attosecond pulses and suggests an experimental resolution of a controversy about the mechanism of energy absorption by rare-gas clusters in strong vacuum-ultraviolet (VUV) pulses.Comment: 4 pages, 3 figure