Herbert Egger (Darmstadt): Analysis and Numerical Methods for
Fluorescence Diffuse Optical Tomography
Wednesday, 10.10.2012 16:15 im Raum SR1B
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
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.