E. Klann (TU Berlin)
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In inverse problems one wants to find unknown parameters or structures by
indirect measurements. Typical inverse problems occur in medical imaging, e.g.,
tomography. The task is to find the inner structure of an object, e.g., a human
torso, from line integrals of some form of radiation that travelled through the
object. In geometric inverse problems one wants to recover this inner structure
also in terms of geometric information, i.e., the number of different interior
objects (bone, liver, lung, etc.), their location and their shape. We present a
Mumford-Shah type functional for the simultaneous reconstruction and
segmentation of an object from tomography data. The minimization of the
functional is realized using shape sensitivity analysis and carried out in the
level-set framework. We show reconstructions and/or segmentations for  several
tomographic applications (SPECT/CT, limited angle tomography, region of
interest CT).