Wednesday, 15:45 - 16:10 h, Room: MA 415

 

Antoine Laurain
A shape and topology optimization method for inverse problems in tomography

Coauthors: Manuel Freiberger, Michael Hinterm├╝ller, Andr'e A. Novotny, Hermann Scharfetter

 

Abstract:
We propose a general shape optimization approach for the
resolution of different inverse problems in tomography. For instance, in the case of Electrical Impedance Tomography (EIT), we reconstruct the electrical conductivity while in the case of Fluorescence Diffuse Optical Tomography (FDOT), the unknown is a fluorophore concentration. These problems are in general severely ill-posed, and a standard cure is to make additional assumptions on the unknowns to regularize the problem. Our approach consists in assuming that the functions to be reconstructed are piecewise constants.
Thanks to this hypothesis, the problem essentially boils down to a shape optimization problem. The sensitivity of a certain cost functional with respect to small perturbations of the shapes of these inclusions is analysed. The algorithm consists in initializing the inclusions using the notion of topological derivative, which measures the variation of the cost functional when a small inclusion is introduced in the domain, then to reconstruct the shape of the inclusions by modifying their boundaries with the help of the so-called shape derivative.

 

Talk 2 of the invited session Wed.3.MA 415
"Optimization applications in industry V" [...]
Cluster 19
"PDE-constrained optimization & multi-level/multi-grid methods" [...]

 

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