Inverse problems and Imaging

The aim of the course is to give a systematic, mathematical introduction to inverse problems in science and engineering. Such problems arise, e.g., in connection with medical imaging, tomography, seismic exploration, and deblurring og images. The course gives the mathematical background for inverse problems and their solution. The theory is illustrated by computational exercises that gives hands-on experience with some common techniques and paradigms.

At the end of the course the learner will be able to: Formulate and identify simple models in the technical sciences, in the form of inverse problems Understand the inherent difficulties of inverse problems Discretize and solve first-kind Fredholm integral equations Understand the mechanisms of regularization for the solution to an inverse problem Implement and use computational tools for the analysis and solution of inverse problems by means of regularization Use different methods for choosing the regularization parameter Implement and use iterative methods for large-scale problems Understand, analyze and solve selected inverse problems in differential euqations Formulate inverse problems in imaging, computerized tomography and electrical impedance tomography Identify nonlinear inverse problems and solve them Explain and utilize the Bayesian approach to inverse problems.

Oral examination and reports. Graded pass/fail only.

Experience with advanced engineering mathematics (e.g. 01035) and numerical computations.

Lectures and exercises with theory and computations.