Differential equation-driven regularization for joint FMT-CT imaging

A primary motivation for multi-modal imaging is to improve reconstructions for low resolution functional modalities using high resolution structural information. Most such approaches assume that the anatomic and functional images share a common physical structure. For fluorescence molecular tomography (FMT), however, this may be only approximately valid. We thus present and analyze a regularization scheme that allows more flexible use of anatomic images. Using parallels between regularization and statistical modeling, we develop a stochastic PDE that shares information across structural boundaries. Simulations indicate that our approach is capable of obtaining more accurate reconstructions than methods treating each tissue independently.