In recent years, optical molecular imaging has attracted increasing attention due to its ability of non-invasive visualization of molecular and cellular processes. As an important optical molecular imaging modality, fluorescence molecular tomography (FMT) is known for its cost-effectiveness and exquisite sensitivity. FMT attempts to reconstruct the 3D spatial distribution of the fluorescent probes inside of small animals based on the photon propagation model, the anatomical structure information, the associated tissue optical properties, and the excitation power and position. Lots of efforts have been made to develop photon migration models, imaging systems and reconstruction strategies. Although much progress has been made, problems still remain in FMT. In this thesis, researches on further improving the accuracy, the robustness and the efficiency of the FMT reconstructions are conducted, and adaptive regularization reconstruction methods for FMT are proposed. The main contributions of this thesis are listed as follows: First, we propose an efficient method with the L1-norm regularization based on coordinate descent to solve the FMT problem with extremely limited measurements. The proposed method minimizes the objective by solving a sequence of scalar minimization subproblems in multi-variable minimization. Each subproblem improves the estimate of the solution via minimizing along a determined coordinate with all other coordinates fixed. This algorithm first updates the coordinate that makes the energy decrease the most. Non-existence of matrix-vector multiplication in the iteration process makes the proposed algorithm time-efficient. The proposed algorithm is able to obtain satisfactory reconstruction results even when the measurements are very limited. Besides,the proposed algorithm is about two orders of magnitude faster than the contrasting algorithm. The numerical experiments validated the high efficiency and reliability. Secondly, we propose an approach based on adaptive matching pursuit for FMT to make reconstruction results more stable and the method easier to use. The proposed algorithm is able to find an optimal sparsity factor and a satisfactory solution always, no matter what value of the initial sparsity factor is estimated. Besides, the proposed algorithm adopts an automatical updating strategy. It ends after only a few iterations and doesn't add extra time burden compared to the stage-wise orthogonal matching pursuit (StOMP) method...
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