Sorbonne Université

Master de Sciences & Technologies

M2 Mathématiques & Applications (Sorbonne Université)

Tomography and inverse scattering

Roman Novikov Ecole Polytechnique

Tomography is known first of all as a research domain related with the problem of determining the structure of an object from X-ray photographs. At present, in addition to this X-ray tomography, several other tomographies are also known, where instead of X-ray photographs some other spectral data are used. In addition, tomographical problems are very much related with problems of inverse scattering. All these problems arise in medical imaging, non-destructive testing and different domains of physics. The objective of this course is to give an introduction to the mathematics of this research domain.

The following topics will be considered, in particular:

  1. X-ray transmission tomography and the classical Radon transform.
  2. Non-abelian Radon transforms and their applications.
  3. Inverse scattering for the multidimensional Schrödinger equation.

References for the course :

  1. F. Natterer, The Mathematics of Computerized Tomography, Wiley, New York (1986)
  2. R. G. Novikov, Non-abelian Radon transform and its applications, https://hal.archives-ouvertes.fr/hal-01772611
  3. R. G. Novikov, Inverse scattering without phase information, Séminaire Laurent Schwartz - EDP et applications (2014-2015), Exp. No 16 (13 pp ); doi: 10.5802/slsedp.74

Preliminary requirements :

Basic knowledge on partial differential equations, Fourier analysis and Cauchy formula of complex analysis.