Fluorescence molecular tomography using a two-step three-dimensional shape-based reconstruction with graphics processing unit acceleration

In fluorescence molecular tomography, the accurate and stable reconstruction of fluorescence-labeled targets remains a challenge for wide application of this imaging modality. Here we propose a two-step three-dimensional shape-based reconstruction method using graphics processing unit (GPU) acceleration. In this method, the fluorophore distribution is assumed as the sum of ellipsoids with piecewiseconstant fluorescence intensities. The inverse problem is formulated as a constrained nonlinear least-squares problem with respect to shape parameters, leading to much less ill-posedness as the number of unknowns is greatly reduced. Considering that various shape parameters contribute differently to the boundary measurements, we use a two-step optimization algorithm to handle them in a distinctive way and also stabilize the reconstruction. Additionally, the GPU acceleration is employed for finite-element- method-based calculation of the objective function value and the Jacobian matrix, which reduces the total optimization time from around 10 min to less than 1 min. The numerical simulations show that our method can accurately reconstruct multiple targets of various shapes while the conventional voxelbased reconstruction cannot separate the nearby targets. Moreover, the two-step optimization can tolerate different initial values in the existence of noises, even when the number of targets is not known a priori. A physical phantom experiment further demonstrates the method's potential in practical applications.