Inverse Problems
Graduate course 2D5245, 7.5 credits, starting Tuesday September 11th (2012) at 13.15-15
in room 3733, KTH (math).
Preliminary Schedule: Thuesdays 13.15 - 15.00, until December, in room 3733, Lindstedtsvagen 25, KTH.
Goal: to understand basic mathematical and
numerical methods to solve inverse problems
related to partial differential equations.
Some topics: ill-posed problems and their
numerical solution by regularization methods,
regularization of linear problems,
Tikhonov regularization,
regularization of non linear problems.
Some applications: differentation as an invers problem,
X-ray tomography, data-assimilation for weather and climate prediction,
inverse scattering, optimal design, image processing,
parameter identification.
Prerequisites: undergraduate differential equations, functional analysis
and numerics.
Literature:
- (Main course book) Heinz W. Engl, Martin Hanke, Andreas Neubauer,
Regularization of Invers Problems, Kluwer Academic Publishers, 2000,
ISBN 0-7923-6140-7 (paperback ~$40), 0-7923-4157-0 ( cloth ~$200);
- Curtis R. Vogel, Computational Methods for Inverse Problems, the Society for Industrial and Applied Mathematics, 2002.
- Albert Tarantola, Inverse Problem Theory, the Society for Industrial and Applied Mathematics, 2005.
- Chapter 9 in Lecture notes on optimal control.
- Zimmer's notes on the spectral theorem for compact operators.
- statistical notes estimators.
- regularization notes for inverse problems.
Plan:
- Introduction and overview.
- Examples and applications
- Regularization for ill-posed linear problems
- Optimal control methods for inverse problems
- Iterative methods and Numerical implementations
Homework:
Here
is a preliminary list of questions to prepare for the exam.
The exam consists of five questions related to
the list.
Presentations:
To pass the course requires atleast 15 credits.
A good answer on a question in the exam gives 2 credits.
A good solution of a homework problem gives 2 credits.
A good presentation gives
5 credits.
Therefore one obtains 25 = 5x2 + 5x2 + 5 credits if
everything is good.
Welcome!
Anders Szepessy,
szepessy@kth.se, 790 7494