"Progress in applications such as medical imaging or astronomy is not only achieved by larger and/or faster equipment (hardware), but also by better algorithms (software). My research deals with the mathematical foundations for the development of new algorithms, e.g., for medical imaging."

Short Curriculum Vitae

2001: Diploma in Mathematics, University of Hamburg, Germany

2006: Ph.D. in Mathematics, University of Bremen, Germany

Former and Current Positions

2001–2006: Research Assistant at the University of Bremen, Germany

2006–2010: Junior Scientist at RICAM, Linz, Austria

2010–2014: Senior Scientist at Johannes Kepler University Linz, Austria

2014-2016: IPODI Fellow at the TU Berlin, Germany

Since 2016: Research Associate at the Institute of Mathematics, Technische Universität Berlin

Research Interests

• Inverse problems
• Regularization methods
• Medical imaging
• Tomography
• Shape sensitivity analysis

Contact

Email: klann[at]tu-berlin.de

Webpage

Numerical analysis of Mumford-Shah type methods for tomography

Duration: 1 November 2014 – 31 October 2016

Mentor: Prof. Dr. Fredi Tröltzsch, Faculty II, Department of Mathematics

Abstract: The goal of tomography is to recover the interior structure of an object (a body or a workpiece) using external measurements. Tomographic imaging techniques are used, e.g., in medicine or non-destructive testing, and are based on several disciplines such as pure mathematics and numerical analysis as well as physics and hard- and software engineering. As existing scanning devices are enhanced (higher resolution, more computational power) and new scanning devices are developed (hybrid imaging, different physical phenomena) the same is necessary for the mathematical reconstruction algorithms. In recent years, so called Mumford-Shah type methods for tomography problems were established. These methods yield a combined output of structural and functional information: not only is an image of the interior computed but also the boundaries or the number of objects within this image. In the proposed project we plan to study those methods further and apply them to tomography problems with limited data such as limited angle or region of interest tomography. We will focus on topics such as (i) parameter choice rules and stopping criteria for the minimization algorithm; (ii) non-negativity and other constraints; (iii) topological sensitivity for inserting new sets.

Output of iterations of a Mumford-Shah level set-based method for simultaneous reconstruction and segmentation of a torso phantom from noisy CT data. Images courtesy of Esther Klann relating to work in E. Klann, R. Ramlau, and W. Ring, Inverse Problems and Imaging, Vol. 5 (2011), 137-166.