Statistical Inverse Problems

In der Zeit vom 20. Juni bis 6. Juli 2005 hielt Herr Prof. B. Mair einen Kompaktkurs, bestehend aus neun Vorlesungen und Übungen, über das Thema "Statistical Inverse Problems". Der Veranstaltungsort war der Seminarraum des Institutes für mathematische Stochastik.



Abstract

"Emission tomography is an important method for functional, molecular imaging of living tissue. It can be used to detect abnormalities in cellular activity before there is any observable anatomical change. It is used to identify many forms of cancer, a damaged heart, and many brain disorders. It is based on the metabolism of various naturally occurring chemicals which are tagged with a radio-isotope. As the isotope decays, the emitted photons are detected and numerical algorithms produce an image of the amount of radiotracer at each location. The direct (non-iterative) filtered back projection algorithm has been the mainstay for reconstructing tomographic images since its inception in the seventies. However, due to the variety of applications requiring relatively short imaging times, and the need for accurate quantitative information, modern scanners now incorporate iterative algorithms based on statistical models and methods. The most common iterative algorithms are modifications of the standard expectation maximization algorithm. As a result, we will pay special attention to this method. We will discuss some of the physics motivating the statistical models, convergence characteristics of the algorithms, and indicate interesting open problems in the area."