The Signal & Image option of the SISEA Master 2

TU1 - Scientific methodology and human training.

 This teaching unit consists of several courses including english, communication, discovery of the industry and research worlds but also how to perform a bibliographical analysis related to a given scientific topic.

TU2 - Scientific bases.

 This teaching unit includes courses of radiocommunications, signal processing and programming.

TU3 - Project.

 A set of master projects in the domain of signal and image processing is proposed to groups of two or three students. Each group will work on it during 18 weeks and will present his results through a one-day seminar.

TU4 - Concepts of information processing.

 This teaching unit proposes three courses. The first one, entitled Kalman filtering and Hidden Markov models, course proposes an introduction in optimal filtering for discrete time systems, i.e. estimating the state of a system from an a priori model and noisy measures. The notion of a priori model is illustrated by examples stemming from the domain of the navigation, the source localization and the pursuit. Two classes of models are considered, for which it is possible to give an exact solution computed in a recursive way: i) the Gaussian linear systems and ii) Markov chains with finite state space. The second course, entitled Optimization, deals with problems of optimization without and with constraints within the theoretical framework of convex optimization and considers their analytical resolution or by means of algorithms making it possible to obtain digital solutions by computer resources. The third course, entitled Detection and estimation theory, is dedicated to estimation theory. The implementation of the various algorithms studied through this teaching unit is the object of several sessions of practicum in MATLAB.

TU5 - Methods for control and data processing.

 This teaching unit is composed of three courses. The first one, entitled Machine learning, is devoted to data fusion and classification. The second one, entitled Inverse problems, aims at showing from a toy example as physical laws used in biomedical engineering allows us to model the observed signals and to formalize a certain class of inverse problems. Unfortunately they are often ill-posed and require to be regularised. Then we show how to interpret and translate mathematically a number of physiological hypotheses in order to perform regularization. Eventually standard approaches (deterministic versus probabilistic) are presented: Tikhonov regularization, LASSO (Least Absolute Shrinkage and Selection Operator) regression, MCMC (Markov Chain Monte Carlo), Gibbs sampling, the Metropolis-Hastings algorithm. They are illustrated through the brain source imaging problem and several sessions of practicum in MATLAB. The third course, entitled Wavelets, deals with the time-scale representations and their link with the harmonic analysis, the approximation of signals and the time-frequency representations.

TU6 - Computational science and engineering.

 The first course of this three-course teaching unit, entitled Filtering methods, aims at characterizing signals based on models, analyzing/filtering signals (predictive, optimal, adaptive, in sub-bands filtering) in the presence or not of noise, and developing generic estimation algorithms. The second course, entitled Image and video processing, is an introduction to image processing. Image transformation, geometric corrections and image enhancement/filtering are considered. The different classes of image segmentation methods are also studied. Movement segmentation and monitoring in image sequences are considered too. The third course, entitled Information theory and image compression, gives the principles and methods for the compression of images and videos. It presents the principal elements of information theory and source coding, the main operators for signal transformation, quantification, prediction, entropic coding, movement estimation/compensation, and flow-distortion optimization. It presents then the principal standards of compression of the images and the videos, which are currently used in all the applications of the everyday life (television, video on demand, streaming, video on mobiles, etc.). It also provides advanced solutions for new methods of imagery like multi-sight and 3D video.

TU7 - Advanced signal and image processing.

 This seventh and last teaching offers a wide panel of courses from which the students will choose four.

Heading of the first proposed module is Geometric and statistical modeling. It rconcerns on one hand the geometrical treatment of 3D images/volumes where the local and global study of curves and surfaces of the 3D space is favored. The pattern recognition is then related to the projection of a 3D form in a description space of lower dimension and to the search of invariants describing locally or globally the 3D objects. It is then possible to define distances between patterns in an elegant way. In addition, this module revisits the problem of image segmentation but this time by using a bayesian formalism. Within this framework, the use of Markov fields is studied. Various algorithmic solutions such as the MCMC method are considered. The course is illustrated using practical examples and exercises. A practicum on the segmentation of cerebral MRI images is also proposed.

The second proposed course, named Medical image registration and GMCAO, aims at giving to the students an overall picture of the computer-assisted medico-surgical gestures. A more specific lighting is brought on the methodological components concerned with the computer vision and the medical image registration.

The third available course is entitled Treatment of video contents and new modalities. It presents mathematical tools and methods allowing for the enrichment and the exploitation of video contents to improve the experience of the user and offer new services. It presents the various models of cameras, the problems of multi-screen capture, calibration of cameras, projective geometry and depiction by the image. It continues by presenting the tools of regularization by diffusion, the various types of methods for image inpainting, video and multi-screen contents. It also presents the various methods of super-resolution by means of examples, the sparse representations and machine learning. It ends with a presentation of methods of indexation and structuring of videos, recognition of actions and visual effects in video.

The fourth proposed course, named Robotic vision and visual subjection. It presents both possible approaches to command the movements of a robot from information supplied by a camera. The first one derives from a fine calibration and the 3D localization of the elements of the system. The second one, said of visual subjection, consists in injecting the visual information as input of a law of closed-loop command. These approaches are general and are illustrated through numerous examples.
The fifth available course is called Blind Source Separation (BSS). Source separation aims at estimating radiocommunication, acoustic, physiological or other kind of sources from linear mixtures or not of the latter. The blind adjective characterizes the absence of knowledge a priori on the aforementioned sources of interest. In electronic war, BSS is used to intercept enemy communications. In audio, the example of the cocktail party shows how from a set of microphones it is possible to isolate the conversations of several groups of people speaking in the same room. In biomedical engineering, BSS allows us to separate the cardiac activity of the mother of that of the foetus from electrocardiographic signals registered on the belly of the mother and to prevent possible cardiac diseases of the foetus. Although Independent Component Analysis ( ICA) was for a long time one of the standards regarding BSS, tensor analysis offers the big interest to be able to process data of low dimensions (for example, case of a low number of time samples). One of the classical tensor decompositions, the canonical polyadic decomposition, is studied and its interest is illustrated in the context of brain source imaging during a session of practical class with MATLAB.
In the context of the design of the command or surveillance systems, obtaining dynamic models of process is an important stage. This sixth course, entitled Modeling and identification, presents the approach and the usual methods of parametric modeling applied to the systems or to the signals: methods of prediction error, variants of the least squares, the model method and subspace approaches.

Finally, a course about radiocommunications and a course dealing with the identification of biomathematical models used in human electrophysiology are also proposed to the students.