Adaptive finite element methods for increased resolution in fluorescence optical tomography

Abstract

ABSTRACT Fluorescence optical tomography is an emerging tool for molecularly based medical imaging. In order to providethe required accuracy and resolution for imaging interior ”uorescent yield and/or lifetime within the tissue,accurate experimental measurements as well as ecient and accurate numerical algorithms are needed.Herein, we present a new adaptive “nite element approach to the inverse imaging problem that is able tosigni“cantly increase the resulting image resolution and accuracy, by (i) using “ner meshes for the parameterestimation where the dye concentration varies signi“cantly, (ii) using “ner meshes for the ”uence predictionwhere gradients are signi“cant, while (iii) choosing coarse meshes in other locations. The nonlinear iterativeoptimization scheme is formulated in function spaces, rather than on a “xed grid. Each step is discretizedseparately, thus allowing for meshes that vary from one nonlinear step to the next. Furthermore, by employingadaptive schemes in the optimization, only the discretization level of the “nal mesh de“nes the achievableresolution, while the initial steps can be performed on coarse, cheap meshes. Using this technique, we cansigni“cantly reduce the total number of unknowns, which not only stabilizes the ill-posedness of the inverseproblem, but also adapts the location and density of unknown parameters to achieve higher image resolutionwhere it is needed. Speci“cally, we use an a posteriori error criterion to iteratively and adaptively re“ne meshesfor both the forward and inverse problems based on derivatives of excitation and emission ”uences as well as thesought parameter. We demonstrate this scheme on synthetically generated data similar to available experimentalmeasurements.Keywords: Image Reconstruction Techniques; Photon Migration; Medical and Biological Imaging; NumericalTechniques; Adaptive Finite Element Methods.