Bioluminescence tomography is in vivo noninvasive imaging methods which can get qualitative and quantitative information of molecular and cellular activity process in the creature body. BLT is to retrieve light source information from the light flux detected on the surface of small animal. While fluorescence molecular tomography is a nonlinear inverse scattering problem, bioluminescence tomography belongs to the inverse source problem due to no demand of external light source and a good signal-to-noise ratio (SNR). To perform BLT experiment, the mice’s main organs are transfected with the reporter gene. This mechanism is currently often used in the real-time study of immune cell trafficking and various genetic regulatory. In Bioluminescence tomography, luciferase enzymes are employed to real-timely in vivo monitor the already tagged cells in living animals. After luciferin is injected into a living animal, those cells in the organism which express the luciferase transgene emit photons of light. Bioluminescent photon propagation in biological tissue is governed by the radiative transfer equation (RTE). However, the RTE is computationally expensive in the practical medical imaging environment. Because the scattering is dominant over absorption in the living animal, the diffusion equation is a relatively accurate approximation and has been widely adopted to describe photon propagation when the biological tissue has characteristic of high scattering optical property. Based on diffusion approximation theory, the uniqueness theorem asserts that BLT reconstruction solution is not unique generally. In view of the ill-posedness characteristic of BLT, we can get many solutions which meet the boundary measured data. In fact, 3D BLT reconstruction is a high ill-posed inverse problem and it is difficult to fully reconstruct the source density information. In order to solve the problem, this dissertation is mainly involved in the following two research areas: 1. A Spatial Weighed Element Based Finite Element Method (SWEFEM) is proposed to raise the accuracy of reconstruction source density. And hence, the reconstruction problem can be transferred to an optimization problem and be solved by some optimization algorithm with simple bounds. 2. This dissertation proposes two optimization algorithms to solve the optimization objective: a tolerant algorithm for linearly constrained optimization and a quasi-Newton method and an active set strategy whose effect is validated in later simulation experiments. 3. Reconstruction-Oriented Multigrid Finite Element Algorithm is proposed to reduce the time cost and variable dimensions of source reconstruction. By setting a threshold as the average reconstruction densities, we can refine every possible source element and form next mesh until the reconstructed densities are accepted.
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