Optimization and Inverse Problems

The majority of scientific and technical applications require the extraction of desired information from previously recorded measured values. Classical examples of this are imaging techniques such as computed tomography, which provide non-invasive information about the inside of a patient or workpiece.

From a mathematical point of view, this process is the solution of an inverse problem and requires careful modelling and analysis of the problem as well as the development of suitable numerical solution methods, which must ensure a balance between accuracy and data error. One approach is the formulation of suitable optimization problems, which are solved by adding problem-adapted penalty terms.