Workshop on Bioimaging II / PDEs, Wed, 21 Nov, 2007
Speaker: Ronny Ramlau
Abstract
In some medical applications, e.g. for the planning of a surgery, it is not only necessary to determine the density distribution of a body but also the accurate boundaries of inner organs. Usually this is done in two steps: First, the density distribution is reconstructed from a CT scan. In a second step the jumps in the reconstruction are determined by image processing methods. In our talk, we propose a variational method that allows to reconstruct both the functional parameters ( the density distribution ) and the geometric parameters (the discontinuity set). We will restrict ourselfs to the reconstruction of piecewise constant functions. The reconstructions will be obtained by the minimization of a Mumford - Shah type functional. We will present analytical results for Computerized Tomography as well as Single Photon Emission Computed Tomography (SPECT). In particular, a regularization theory for our method will be developed. We will give numerical results for both applications. This talk is joint work with Wolfgang Ring (University of Graz, Austria) and Esther Klann (Radon Institute, Linz, Austria).
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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