Inverse problems

Course content

The students understand the of the complex links between their previous mathematical knowledge and the contents of the lecture,
understand the theoretical body of the lecture as a whole and master the corresponding methods, are able to analyze and apply the methods of the lecture, know and understand the notion of well- and ill-posedness and of regularization methods and their properties, are able to understand, analyze and apply methods to approximately solve ill-posed problems and use them with mathematical software.

Content

• Compact operators, pseudo inverse
• Regularization methods, order optimality
• Tikhonov regularization, Landweber iteration, the CG method
• A-priori and a-posteriori parameter choice
• Nonlineare Problems, convex variational regularization methods