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Amit
Joshi, Wolfgang Bangerth, Eva Sevick-Muraca

**Adaptive finite element modeling of optical
fluorescence-enhanced tomography**

Optics Express, vol. 12 (2004), pp. 5402-5417.

A three-dimensional fluorescence-enhanced optical tomography scheme based
upon an adaptive finite element formulation is developed and
employed to reconstruct fluorescent targets in turbid media from
frequency-domain measurements made in reflectance geometry using
area excitation illumination. The algorithm is derived within a
Lagrangian framework by treating the photon diffusion model as a
constraint to the optimization problem. Adaptively refined meshes
are used to separately discretize maps of the forward/adjoint
variables and the unknown parameter of fluorescent yield. A
truncated Gauss-Newton method with simple bounds is used as the
optimization method. Fluorescence yield reconstructions from
simulated measurement data with added Gaussian noise are
demonstrated for one and two fluorescent targets embedded within a
512 ml cubical tissue phantom. We determine the achievable
resolution for the area-illumination/area-detection reflectance
measurement geometry by reconstructing two $0.4cm$ diameter
spherical targets placed at at a series of decreasing lateral
spacings. The results show that adaptive techniques enable the
computationally efficient and stable solution of the inverse
imaging problem while providing the resolution necessary for imaging
the signals from molecularly targeting agents.

*Wolfgang Bangerth*

* Wed Apr 19 13:44:46 MDT 2017 *