Study Of Reconstruction Technologies For Fluorescent Molecular Tomography

The fluorescent molecular tomography (FMT) is one of the most important molecular imaging modalities. In such an imaging modality, a fluorescent probe is used as the contrast agent, which will emit the fluorescent light under the illumination of the excitation sources. The distribution images of the absorption coefficients, the scattering coefficients, the fluorescence quantum efficiency as well as the fluorescence lifetime inside the tissues are reconstructed through the measurements of light on the surface of the tissues in combination with a proper photon propagation model in the tissues. The advantages of FMT lie in its no radiative injury, low cost, simple equipment and so on. It can be potentially used in many fields such as gene expression, tumor detection, protein molecular detection as well as the detection of the functional changes in bodies, and hence it is of great value for research. In this thesis, the reconstruction algorithms for the FMT are studied. The main work and contributions are as follows:Image reconstruction of FMT often involves repeatedly solving large-dimensional matrix equations, which are computationally expensive. In this thesis, the forward equations of the FMT are modeled within the finite element method framework. A wavelet-based multi-resolution reconstruction approach is proposed for the FMT reconstruction in combination with a parallel forward computing strategy, in which both the forward and the inverse problems of FMT are represented in the wavelet domain. By means of the multi-resolution representation scheme, both the forward and the inverse problems are solved in a fine-to-coarse-to-fine procedure. Simulation results demonstrate that the proposed method can speed up the reconstruction process with improved reconstruction accuracy. Furthermore, such a method is especially suitable for the case where there are large deviations in the optical properties between the target and the reference medium.For the purpose of improving the rate of convergence of the reconstruction algorithm, a tree structured Schur complement decomposition strategy is proposed. The most important feature of this method lies in the fact that the global system is decomposed level by level with the Schur complement system along the two paths in the tree structure and the subsystems are solved in combination with the biconjugate gradient method. Upon performing the Schur complement decomposition, the condition number of the subsystem can be reduced, and therefore the process of obtaining a solution to a system of matrix equations with a given precision can be accelerated. The Tikhonov regularization method is used for tackling the ill-posedness of the reconstruction problem, for which an adaptive strategy is proposed to determine the regularization parameters, where the regularization parameters are adaptive not only to the spatial variations but also to the variations of the objective function.A novel innovative region-based method is proposed to reduce the unknowns involved in the reconstruction and hence to improve the efficiency of the reconstruction. This method classifies the image to be reconstructed into the target areas and the background area and assigns constant value to the property in the interior of a region. The target areas are determined by searching for the nearest neighbor nodes of them. The proposed method can lead to a significant reduction of the unknowns involved in the reconstruction. Owing to the significant reduction of the unknowns in our region-based reconstruction method, we proposed to incorporate the Hessian matrix (second-order derivatives) in the optimization to accelerate the convergence of the algorithm. We also proposed a multi-wavelength reconstruction strategy, which employs the excitation and emission light measurements in turn for iterative computation.During the process of the image reconstruction of FMT, the Jacobian matrix needs to be computed repeatedly with huge computational requirements. Therefore, we proposed an effective method to solve the Jacobian matrix. In this method, the columns with the sum of the absolute value of the elements lower than the threshold will be deleted. Thus, the Jacobian matrix can be simplified and the size of the matrix is reduced, which can improve the efficiency of the matrix computation. Simulation results demonstrate that the proposed method can speed up the process of matrix computation and thus significantly improve the efficiency of reconstruction.