Conference on Applied Inverse Problems, July 20-24, 2009, Vienna, Austria
Poster Presentation
Manuel Freiberger: Application of level-set type reconstruction to fluorescence optical tomography

Mon, 20 July, 2009, 17:15-18:15, Foyer

Fluorescence diffusion optical tomography (FDOT) is one of the newer imaging technologies showing a huge potential for medical applications. It utilizes a set of sources placed on the surface of the sample under investigation to inject light into the object. The light is scattered into the tissue and absorbed by a fluorescent dye which re-emits part of the photons at a higher wavelength. These photons propagate through the tissue again and are measured on the boundary. From these boundary measurements, the distribution of the fluorophore shall be reconstructed. Regularization methods are needed as this problem is severely underdetermined and ill-posed.
In our contribution we investigate the application of quasi level-set methods to FDOT. Level-set methods are advantageous whenever a good a-priori choice of the parameter values inside the perturbation and the background is available and only the shape of the perturbation has to be reconstructed. Furthermore, the distinct boundary of the perturbation in the reconstruction offers the possibility to easily discriminate the background from the object which is needed in certain medical settings like the determination of the position and size of a tumour.
The level-set type approach implemented is based on a differentiable approximation of the level-set function where the approximation quality can be controlled by a parameter. For the reconstructions an iteratively regularized Gauss-Newton scheme is used, thus decreasing the influence of regularization in each iteration. Additionally, the approximation quality of the differentiable functional is increased in every step such that the reconstructions from the quasi level-set method approaches the true level-set result.
Quasi level-set regularization shows promising results when compared to conventional regularization methods like a L2-penalty term. Currently the quality of the result is limited by the size of the mesh elements. It is expected that adaptive mesh refinement will overcome this limitation to provide more correct reconstructions. Open problems are still the a-priori choice of the parameter niveaus and the implementation of a stopping criterion.

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