Wolfgang Bangerth, Amit Joshi, Eva
Sevick-Muraca
Adaptive finite element methods for increased
resolution in fluorescence optical tomography
Progress in Biomedical Optics and Imaging, vol. 6 (2005),
pp. 318-329.
Fluorescence optical tomography is an emerging tool for
molecularly based medical imaging. In order to provide the required
accuracy and resolution for imaging interior fluorescent yield and/or
lifetime within the tissue, accurate experimental
measurements as well as efficient and accurate numerical algorithms are
needed.
Herein, we present a new adaptive finite element approach to the
inverse imaging problem that is able to significantly increase the
resulting image resolution and accuracy, by (i) using finer meshes for
the parameter estimation where the dye concentration varies
significantly, (ii) using finer meshes for the fluence prediction where
gradients are significant, while (iii) choosing coarse meshes in other
locations.
The nonlinear iterative optimization scheme is formulated in function
spaces, rather than on a fixed grid. Each step is discretized
separately, thus allowing for meshes that vary from one nonlinear step
to the next. Furthermore, by employing adaptive schemes in the
optimization, only the discretization level of the final mesh defines the
achievable resolution, while the initial steps can be performed on
coarse, cheap meshes. Using this technique, we can significantly
reduce the total number of unknowns, which not only stabilizes the
ill-posedness of the inverse problem, but also adapts the location and
density of unknown parameters to achieve higher image resolution where
it is needed. Specifically, we use an a posteriori error criterion to
iteratively and adaptively refine meshes for both the forward and
inverse problems based on derivatives of excitation and emission
fluences as well as the sought parameter. We demonstrate this scheme on
synthetically generated data similar to available experimental
measurements.
Wolfgang Bangerth
Sat Apr 20 09:13:53 MDT 2024