65-457 Variational methods for inverse problems (in English)

Instructors: Prof. Dr. Anna Christina Brandt

Event type: Lecture

Displayed in timetable as: M-VMMOA-V

Hours per week: 4

Language of instruction: English

Min. | Max. participants: - | -

Comments/contents:
Important notes



1)  The course "Optimization" will be given together with the course   "Variational methods for inverse problems", i.e. students of both course will have the lecture on optimization together. The second lecture on Thurday morning is just for participants of the Variational methods for inverse problems"  However, please do not register for both courses! You need to decide for one of the two course options!

2) There is one joint Moodle course for both lectures named
         Optimization & inverse problems

The password for participants of  this part of the course ("Inverse problems" ) is: Tikhonov_23

All other relevant course information you will find in the Moodle course. Please read carefully the general information.
 

Learning objectives:
The course will treat the classical theory for linear inverse problems as well as variational methods for reconstruction. 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

• Ill-posed operator equations
  
• Regularization of linear inverse problems
  
• Variational methods: Tikhonov - type regularization, minimization algorithms
  
• Variational regularization: theory from convex optmization
  
• Outlook: nonlinear inverse problems