Invited Session Thu.2.MA 649

Thursday, 13:15 - 14:45 h, Room: MA 649

Cluster 24: Variational analysis [...]

Variational methods in inverse problems


Chair: Elena Resmerita



Thursday, 13:15 - 13:40 h, Room: MA 649, Talk 1

Esther Klann
A Mumford-Shah type approach for tomography data


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).



Thursday, 13:45 - 14:10 h, Room: MA 649, Talk 2

Mihaela Pricop-Jeckstadt
Genomic selection and iterative regularization methods

Coauthor: Norbert Reinsch


In genomic selection it is expected that genetic information contributes to selection for difficult traits like traits with low heritability, traits which are hard to measure or sex limited traits.
The availability of dense markers covering the whole genome leads to genomic methods aiming for
estimating the effect of each of the available singlenucleotide polymorphism. Hence, we propose a semiparametric method and an iterative regularization approach for high-dimensional but small sample-sized data. Numerical challenges like model selection, the estimation of the predictive ability and the choice of the regularization parameter are discussed and illustrated by simulated and real data examples.



Thursday, 14:15 - 14:40 h, Room: MA 649, Talk 3

Christiane Pöschl
TV-denoising and evolution of sets

Coauthors: Vicent Caselles, Matteo Novaga


Let S ⊂ R2 be the union of two convex sets with smooth boundary.
We connect the levelsets of the minimizers u\lambda of
1⁄2 || u-χS || L22 + λ || u ||TV
to the minimizers of a (simpler) set-minimization problem in order to obtain a geometrical
characterization of the levelsets of u\lambda.
Moreover, we calculate explicit minimizers of (1),
when S is the union of two nonintersecting circles/squares, using
simple morphological operators.
We also show how to construct the solutions for the more general case when S
is nonconvex, starshaped set.


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