Research Topics
Nonstationary signal processing
The group has a strong history of studying nonstationary signal processing, ranging from theoretical analalysis or development of approaches such as time-frequency methods, data-driven decompositions (e.g., Empirical Mode Decomposition), practical characterization of stationarity and non-stationarity. Many applications of these methods have been put forward as well by the group.
Scale invariance, multifractals and wavelets
Scale invariance analysis and modeling has been a long standing research topic within SiSyPh team. Significant efforts have been and still are devoted to the definition, design and practical synthesis of stochastic processes with prescribed scaling properties, combined either to other statistic properties (distributions, dependencies) or to geometrical properties (free divergence, prescribed curl,...) to match a given application field (mainly hydrodynamic turbulence). Statistical signal processing tools are also designed and studied theoretically and practically, aiming to test the existence of scale invariance, to estimate scaling parameters or the scaling range bounds. The recent focus is on multivariate signals, and multidimensional fields with possible anisotropy.
Graph signals and complex networks
Data appear often with a mixture or relational properties –coded by graphs or networks–, and attributes —naturally dealt as signals (possibly multivariate signals). An activity of the group is to study signal an ddata processing for these types of data, both for graph signals (when a signal is indexed by a graph) and for complex networks where the signal of interest is the network itself. In both cases, the group has a specific interest in networks which are dynamic, or for which a multiscale approach is fruitful.
Inverse problems in imaging
The group has recently developed an activity focused on the resolution of inverse problems and optimisation. The inverse problems we consider can be split in three topics : - Image restoration - Non-stationarity and optimisation - Change-point detection and segmentation for regularity estimation
Biomedical image and signal processing
SiSyPh research team is putting significant efforts into developing signal/image processing tools for biomedical applications. On the image processing side, an efficient reconstruction procedure mixing on non-smooth convex optimization to balance data fidelity and regularization provides an efficient reconstruction procedure for high resolution image from low resolution records. On the signal processing side, statistical tools are customized to analyze scale invariance in heart rate variability (notably in the context of intrapartum fetal heart beat analysis) as well as in infraslow brain activity. It notably permits to relate scale invariance in background brain activity to functional connectivity and to quantify task-rest modulation of brain scaling.
Statistical physics, signal processing and information theory
We apply concepts from Statistical Physics, nonlinear Physics and Information Theory to define or refine signal processing tools.
Analyses of social and human activities
The avalanche of digital data tracing social activities opens the way to combine data analysis and modeling with social science studies. Along this line, we study data representing human interaction or behaviour, or date pertaining to transportation (e.g., BSS or traffic on roads); in all these cases, the dynamics of the data (for instance of the networks uwed to represent them) is crucial and tailored methods are developed leveraging on methods in physics and/or signal processing.
Fluid turbulence, quantum fluids
La turbulence des fluides et le traitement du signal sont des domaines intimement liés. D'une part, les mesures expérimentales d'un écoulement turbulent, et les simulations numériques des équations de Navier-Stokes, ont bénéficié des techniques et développements de la science du signal. D'une autre part, la nécessité de prendre en compte l'aspect multidimensionel des grandeurs liées à la turbulence, et la volonté de construire des modèles aléatoires capables de rendre en compte des statistiques particulières observées dans les écoulements, est un territoire fécond pour le développement d'approches multivariées des signaux. L'équipe Sisyphe depuis longtemps s'attèle à développer ce domaine pluridisciplinaire.
Internet traffic and networks
The team has studied the statistics of the IP trafic over the Internet networks, both from modeling and experimental (monitoring) points of view. Results about the statistics of IP traffic were obtained (such models with Long Range Correlations) and pratical applications such as classifaction of traffic and host or anomaly detection were developed.