Fachbereich Mathematik 
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Inverse problems (Winter term 2018)

The course will treat the classical theory for linear inverse problems. Inverse problems occur in many applications in physics, engineering, biology and imaging. Loosely speaking, solving the forward problem consists of computing the outcome of a known model given the model parameters. The inverse problem consists of computation of the unknown parameter of interest given the physical model and noisy measurements of the outcome. Typical examples are parameter identification problems such as computer tomography, deconvolution problems, denoising of images etc. In particular the following topics are discussed:

  • Examples of ill-posed inverse problems
  • Reconstruction in Computer tomography
  • Ill-posed operator equations
  • Regularization of linear inverse problems
  • Iterative reconstruction methods
  • Tikhonov - regularization

Note: The first part of the course will take place together with the course about computer tomography.

Exercises:

  • One exercises sheet every week;
  • The exercises consits of both theoretical and computer (Matlab) exercises.
  • You need to mark at least 60% of the overall exercises and 50% of the computer exercises.

Actual exercise sheet: Exercises

Exams:

    Exam will take place in February 2019.

Literature:

  • Engl, Hanke, Neubauer, Regularization of inverse problems
  • Rieder, Keine Probleme mit inversen Problemen
  • Hansen, Discrete inverse problems
  • Louis, Inverse und schlecht gestellte Probleme
  • Mueller, Siltanen, Linear and nonlinear inverse problems with practical applications
  • T.G. Feeman, The mathematics of medical imaging, Springer, 2010
  • F. Natterer, The Mathematics of Computerized Tomography, Classics in Applied Mathematics 32,,SIAM, 2001

Other useful material


 
  Seitenanfang  Impress 2018-09-26, Christina Brandt