Development statistical methods for signal and image processing

Presentation of scientific activities

The difficulty lies in the diversity of this information which can concern the structure of the unknown variables or the data, their orders of magnitudes or, in a dynamic context, the way they evolve over time.

On the one hand, the objective is to propose relevant models to represent the information at hand. On the other hand, part of our work consists in developping optimal estimators based on these models along with algorithms to calculate them. Three main applications have been considered so far : localization and tracking, digital communications and biomedical engineering.

Localization/navigation and tracking

In navigation, a vehicle calculates its own position from embedded sensors whereas tracking consists in an external sensor which computes the trajectories of a set of targets. In both cases, the issue is to estimate a set of parameters which vary through time and represent the dynamics of a set of mobiles. Different issues may arise but the team is more particularly interested in the following topics.

In a general manner , choice and tuning of the motion models, including

study of metrics to assess the similarity of different models,
in the case of maneuvers, Bayesian non parametric models to allow the mobiles to switch between an a priori unlimited number of dynamic models,
taking intrinsically into account constraints. For instance, in vision based localization, the pose of the camera lies in a Lie group.

In GPS navigation, modelization of the multipath error and more specifically

use of copula to represent spatial correlations between the different satellite measurements,
Bayesian non parametric models to deal with the strong multimodality of the error in an urban context.

In multitarget tracking, presence of false alarms, missed detection and uncertainties on the association of the measures to the targets. Proposed solutions consists in

developing algorithms to improve the detection in the presence of clutter and thermal noise.
Improving the range/Doppler profiles through time-frequency analysis.
Tracking algorithms based on random finite sets theory.

Biomedical engineering : proteomics

A new generation of clinical research methods, based on proteomic analysis, is currently emerging either for diagnosis or pronostic. The objective is to characterize some diseases by specific signatures on protein profiles. Two main issues are : the early detection of deseases and an individualized treatment. They are based on the discovery of biomarkers. A for these issues, from a data processing point of view, one of the challenges is to develop a model selection method.

We work in a bayesian framework which leads to optimal selection functions. They rely on the computation of evidences, which is a well-known difficult task. We present analytical expressions, eiher exact or approximated. In the end, we take into account both technological and biological variabilities. We study their impact on the performance of the biomarker discovery methods (type I and type II errors). This is a crucial step in the development and exploitation of these analysis chains.

Digital communications

New communication standards are more and more stringent as for the spectral and energetic efficiency of the communicating systems. In this context, our contributions deal with massive multi-antenna systems

source detection and localization, spatial multiplexing
better than Nyquist systems : pulse shape, PAPR, equalization and turbo-processing. systèmes communicant au delà du rythme de Nyquist : forme d’onde, PAPR, égalisation et turbo traitements
cognitive radio : exploitation of HARQ primary protocols for secondary users, inter OSI layer optimization (resource allocation for HARQ protocols)
numerical signal processing to compensate distorsions from the RF layer (power amplifier) or at the edge between numerical and analogical layers (very high frequency A/N conversion)

Spectral Skills

Bayesian inference

optimal filtering

time-frequency analysis

source detection and localization

Monte Carlo estimation

model selection

inverse problems

Spectral

Presentation of scientific activities

Localization/navigation and tracking

Biomedical engineering : proteomics

Digital communications

Spectral Skills

Latest news from the team

Staff

Contact our team