Herbert Egger (Darmstadt): Analysis and Numerical Methods for Fluorescence Diffuse Optical Tomography

Mittwoch, 10.10.2012 16:15 im Raum SR1B
Mathematik und Informatik

Diffuse optical tomography is a biomedical imaging technique that aims at recovering the distribution of physiologically relevant optical parameters of biological tissue from boundary measurements of light propagation through an object. The presence of fluorescence markers allows to distinguish between excitation and emission ligth, thus increasing the SNR of the recorded signals. The interaction of the fluorescence markers with the underlying tissue additionally enables to image physiological activity. After a short discussion of the basic models for light propagation in highly scattering media, we formultate three forward models that describe the illumination of object by excitation light, the absorbtion and re-emission of light by the fluorophores, and the back propagation and recording of the emitted light at the surface. Basic properties of the forward operater which maps the flurophore concentration to the recordes signals will be derived. Based on a linearized model, we then show uniqueness of the corresponding inverse problem which consists of determining the distribution of the fluorophores from light measurements on the boundary. In the third part of the talk, we discuss the solution of the inverse problem by Tikhonov regularization. We first verify the basic assumptions that are required to ensure convergence of the regulariztion method and then discuss the systematic discretization via Galerkin finite element methodsvwhich allow the exact computation of gradients via adjoint equations. A reformulation of the optimality condition is utilized to further accelerate the reconstruction procedure and some numerical results will be presented to illustrate the efficiency of the proposed methods.

Angelegt am Montag, 08.10.2012 11:52 von mburg_01
Geändert am Montag, 08.10.2012 11:52 von mburg_01
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