Thursday, 13:15 - 13:40 h, Room: MA 649

 

Esther Klann
A Mumford-Shah type approach for tomography data

 

Abstract:
We present a Mumford-Shah-type approach for the simultaneous reconstruction and segmentation of a
function from its tomography data (Radon transform). The sought-after function is modeled as a
piecewise constant function. Hence, it consists of~n sets~Ωi and the corresponding
values~ci. The sets and values together with their number are found as minimizers of a
Mumford-Shah-type functional. We present a level-set based minimization algorithm for this
functional as well as theoretical results regarding the existence of minimizers, stability and
regularization properties. We also present numerical results for tomography problems with limited
data (limited angle, region of interest and electron tomography).

 

Talk 1 of the invited session Thu.2.MA 649
"Variational methods in inverse problems" [...]
Cluster 24
"Variational analysis" [...]

 

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