Dieses Dokuwiki verwendet ein von Anymorphic Webdesign erstelltes Thema.

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
someotherpage [2013/01/31 19:33]
desbat
someotherpage [2013/01/31 19:48] (current)
desbat
Line 1: Line 1:
-====== Lectures ======+====== ​IAM Lectures ======
  
  
Line 43: Line 43:
 for addressing such problems are described in this course. ​  These methods are based  for addressing such problems are described in this course. ​  These methods are based 
 either on optimal control theory or on statistical estimation theory. either on optimal control theory or on statistical estimation theory.
 +
 +===== (N) Numerical methods for hyperbolic equations ===== 
 +3 ECTS, L. Debreu and G.H. Cottet
 +
 +This course will cover the design and numerical analysis of finite­volume methods for 
 +conservation ​  ​laws. ​  ​It ​  ​will ​  ​first ​  cover the   ​essential ​  ​properties ​  ​of ​  ​the ​  ​underlying ​
 +mathematical ​ models (conservation,​ entropy conditions, ​ maximum ​ principle...). ​ It  will 
 +then   ​describe ​  ​the ​  ​classical ​  ​schemes ​  ​(upwind, ​  ​Lax­Wendroff...) ​  ​and ​  ​the ​  ​techniques ​  ​to ​
 +derive TVD and high order methods. The properties of the methods will be illustrated in 
 +applications in fluids mechanics and geophysics.
 +
 +===== (N)   ​Optimal Transport, level­set: applications to biophysics =====
 +3 ECTS, E.Maître ​
 +
 +This lecture will link level­set modeling of biomechanical systems (e.g. immersed elastic  ​
 +membranes ​  ​mechanics) with   ​optimal transportation ​  ​theory. ​  ​Interpolation ​  ​algorithms ​
 +based on physical knowledge of images content will be studied. Theoretical as well as 
 +practical implementation aspects will be considered.
 +
 +===== (N)   ​Mathematical ​  ​methods ​  ​for ​  ​wave ​  ​propagation: ​  ​application to inverse problems and medical imaging =====
 +3 ECTS,  E. Bonnetier and F. Triki.
 + 
 +This  course ​ studies ​  ​the ​  ​propagation ​  ​of ​  ​electromagnetic ​  ​waves, ​  ​described ​  ​in ​  ​harmonic ​
 +regime ​  ​by ​  ​the ​  ​Maxwell ​  ​equations, ​  ​and, ​  ​in ​  ​some ​  ​particular ​  ​case, ​  ​by ​  ​the ​  ​Helmholtz ​
 +equation. ​ We first present mathematical tools for such equations, then inverse problems ​
 +like impedance tomography and magnetic resonance imaging.
 +
 +===== (I) Modélisation surfacique (36h – S. Hahmann et F. Hétroy) ===== 
 +
 +=====  (I)   ​Medical ​  ​Imaging: ​  ​tomography ​  ​and ​  ​3D ​  ​reconstruction ​ from 2D projections =====
 +3ECTS, L. Desbat
 +
 +CT   ​Scanners ​  ​and ​  ​nuclear ​  ​imaging ​  ​(SPECT ​  ​and ​  ​PET) ​  ​have ​  ​greatly ​  ​improved ​  ​medical ​
 +diagnoses and surgical planning. ​  ​Mathematics is necessary for these medical imaging ​
 +systems ​  ​to ​  ​deliver ​  ​images. ​  ​We ​  ​present ​  ​mathematical ​  ​problems ​  ​arising ​  ​from ​  ​these ​
 +medical imaging systems. We show how to reconstruct images from projections of the 
 +attenuation function in radiology or respectively of the activity in nuclear imaging. We 
 +present recent advances in 2D and 3D reconstruction problems.
 +
 +===== (I) Wavelets and applications =====
 +3ECTS, Valérie Perrier
 +
 +Wavelets are basis functions widely used in a large variety of fields: signal and image 
 +processing, numerical schemes for partial differential equations, scientific visualization.
 +This course will present the construction and practical use of the wavelet transform, and 
 +their   ​applications ​  ​to ​  ​image ​  ​processing :   ​Continuous ​  ​wavelet ​  ​transform, ​  ​Fast ​  ​Wavelet ​
 +Transform (FWT), compression (JPEG2000 format), denoising, inverse problems.  ​
 +The theory will be illustrated by several applications in medical imaging (segmentation, ​
 +local tomography, ...).
 +
 +
 +===== (I) Advanced Imaging =====
 +3ECTS, Sylvain Meignen
 +
 +In this course, we will first focus on linear methods for image denoising. In this regard,  ​
 +we will investigate some properties of the heat equation and of the Wiener filter. We will  ​
 +then introduce nonlinear partial equations such as the Perona­Malick model for noise 
 +removal, and some other similar models. A last part of the course will be devoted to edge 
 +detection for which we will consider the Canny approach and, more precisely, we will deal 
 +in details with active contours and level sets methods.
 +
 +This   ​presentation ​  ​covers ​  ​2D ​  ​tomography ​  ​including ​  ​the ​  ​reconstruction ​  ​of ​  ​Region ​  ​Of ​
 +Interest from non­complete data (very short scan trajectories,​ truncated projections),​ 3D 
 +tomography ​  ​from ​  ​Orlov ​  ​and ​  ​Tuy ​  ​conditions ​  ​to ​  ​Kolsher ​  ​filter ​  ​and ​  ​Katsevich ​
 +reconstruction formula, and dynamic tomography.
 +In  the introduction ​ we present ​  ​briefly the  physical ​ interactions ​  ​between ​ photons ​  ​and ​
 +matter. We derive the mathematical problem formulation of a function reconstruction ​
 +from its projections. We introduce the Radon transform and the x­ray transform, their 
 +basic   ​properties, ​  ​in ​  ​particular ​  ​the ​  ​Fourier ​  ​slice ​  ​theorem. ​  ​In ​  ​2D ​  ​tomography, ​  ​we ​
 +demonstrate the Filtered Back Projection inversion formula and its application to fan­
 +beam geometries. We then concentrate on recent advances in ROI reconstruction from 
 +incomplete ​  ​projections. ​    ​In ​  ​3D ​  ​reconstruction, ​  ​we ​  ​derive ​  ​inversion ​  ​conditions ​  ​and ​
 +formulas ​ for  the  parallel ​ geometry ​ and  the  Cone  Beam  Geometry. ​  We develop ​ recent ​
 +advances based on the Katsevich formula. ​  We then introduce dynamics problems, i.e. 
 +reconstruction ​  ​from ​  ​dynamic ​  ​objects. ​    ​We ​  ​consider ​  ​the ​  ​problem ​  ​reconstructing ​  ​a ​  ​2D ​
 +dynamic object from its projections and show extensions to 3D dynamic reconstruction.
 +
 +
 +==== (I) Visualisation scientifique (18h – G.P. Bonneau) ====
 +
 +
 +
 +===== (S) Kernel methods in machine learning =====
 +3ECTS 18h, Teacher: Zaid Harchaoui (zaid.harchaoui@gmail.com)
 +
 +Objectives: ​  ​To ​  ​provide ​  ​an ​  ​introduction ​  ​to ​  ​kernel ​  ​methods ​  ​in ​  ​Statistics ​  ​for ​  ​machine ​
 +learning.
 +Prerequisites: ​  ​The ​  ​minimal ​  ​prerequisites ​  ​for ​  ​this ​  ​course ​  ​are ​  ​a ​  ​mastering ​  ​of ​  ​basic ​
 +Probability theory for discrete and continuous variables and of basic Statistics.
 +Schedule: to be precised.
 +Textbooks/​references:​ to be precised.
 +
 +===== (S) Computational statistics in biology and medicine =====
 +3ECTS, (C 18H), Lecturers: O. François and JB Durand/G Bouchard ​
 +
 +Corresponding to the french UE (Ensimag): « Algorithmes et statistique »   
 +Computational statistics concerns the application of algorithmic techniques to problems ​
 +in statistics and in the analysis of large data sets. At the interface between computer ​
 +science and statistics, this field addresses a large number of applications in biology and 
 +medicine. ​ This course will give an overview of methodological and practical approaches ​
 +in computational statistics with applications to epidemiology,​ genetics or medical signal ​
 +analysis.
 +
 +===== (S) Point processes, reliability and survival analysis =====
 +3ECTS, O Gaudoin ​
 +
 +Random ​  ​point ​  ​processes ​ are  used   ​for ​  ​modeling ​  ​the ​ occurrence ​ of   ​recurrent ​  ​events ​  ​in ​
 +time. Their study has multiple applications in the areas of health, industry, demography, ​
 +actuarial ​  ​science, ​  ​etc... ​  ​The ​  ​objective ​  ​of ​  ​this ​  ​course ​  ​is ​  ​to ​  ​present ​  ​the ​  ​essentials ​  ​of ​
 +stochastic modeling and statistical inference for such processes. The preferred fields of 
 +application will be reliability and survival analysis.
 +
 +
 +===== (S) Time Series Analysis =====
 +3ECTS, A. Latour
 +
 +This course attempts to provide a comprehensive introduction to time series analysis. It 
 +gives an account of linear time series models and their application to the modeling and 
 +forecasting of data collected sequentially in time. A time series is a sequence of random ​
 +variables Xt, the index t in Z being referred to as “time”. Typically the observations are 
 +dependent and one aim is to predict the “future” given observations X1, . . . , Xn in the  ​
 +“past”. Although the basic statistical concepts apply  (such as likelihood, mean square ​
 +errors, etc.) the dependence must be taken into account. In the spirit of Brockwell and  ​
 +Davis (1991), the approach is based on elementary Hilbert space methods.
 +
 +
 +==== (S) Reconnaissance des formes et apprentissage (18h – J.B. Durand) ====
 +==== Reconnaissance des formes et apprentissage (18h – J.B. Durand) ==== 
 +==== Méthodes de Monte-Carlo en finance (18h – J. Lelong et M. Echenim) ​ ==== 
 +==== Fondements mathématiques du calcul stochastique (36h – P. Etore) ==== 
 +==== Gestion dynamique des risques financiers 1 (18h – P. Etoré) ​ ==== 
 +==== Calcul stochastique avancé (18h – P. Etoré) ==== 
  
someotherpage.txt · Last modified: 2013/01/31 19:48 by desbat
Dieses Dokuwiki verwendet ein von Anymorphic Webdesign erstelltes Thema.
www.chimeric.de Valid CSS Driven by DokuWiki do yourself a favour and use a real browser - get firefox!! Recent changes RSS feed Valid XHTML 1.0