Algorithms Based On Prior And Error Compensation For Fluorescence Molecular Tomography

FMT is a kind of macroscopic optical molecular imaging technique which can be used for functional imaging of live small animals non-invasively;it has been widely used in early tumor detection,drug discovery and many other biomedical research fields.FMT reconstructs the 3D distribution of fluorophore inside small animal by solving the forward problem and inverse problem.Since the inverse problem of FMT is highly ill-conditioned,experimental noises and errors in forward problem will severely deteriorate the reconstruction results.To comprehensively improve the quality of FMT's reconstruction images,we did algorithm researches in three aspects:Improving the accuracy of the forward problem of FMT,overcome the ill-condition of the inverse problem of FMT,and compensating for the error induced by inaccurate modelling of optical properties.This thesis presented a FEM solution of the forward problem of FMT based on Born approximation,and by labelling the mesh nodes according to their voxel coordinates,anatomical structure was incorporated into the solution as prior information.FMT/CT imaging experiment on small animal was conducted to compare the simulated excitation and emission intensity distribution obtained by FMT and FMT/CT with measured data respectively.The results showed that the relative error of excitation in the former case is 34.08%,23.85%in the latter case,and the relative error of emission in the former case is 33.12%,20.94%in the latter case,which validated that the accuracy of FMT's forward problem was improved by incorporating structural prior provided by CT.To overcome the ill-condition of FMT's inverse problem,this thesis proposed a new algorithm for FMT image reconstruction based on iteratively reweighted L1 regularization and split Bregman method.Compared to commonly used L1 regularization,this new algorithm is able to further enhance the sparsity of solution and needs less measurements theoretically.Phantom experiment was conducted and its results showed that the new algorithm was still able to restrain artifacts in reconstruction images with limited measurements and improve the location accuracy of fluorophore.To compensate for the error caused by inaccurate modelling of optical properties in solving the forward problem,this thesis proposed a parameter-variable prior BAE method based on Bayesian statistical inference.This new method can promote the sparsity of solution by dynamically adjusting the parameter of prior.Quantitative analysis of the results of small animal experiment showed that this new method performed better in restraining artifacts caused by inaccurate modelling of optical properties,and in recovering the shape of fluorophore than traditional BAE method.To improve the efficiency of BAE-based FMT image reconstruction algorithms,this thesis proposed a small sample BAE method.This new method uses PCA to compress the forward matrix and measurements based on the correlation between rows of the forward matrix,and thus the number of samples needed in estimating the parameters of errors are reduced.Simulation study and experiment on small animal verified that small sample BAE method was able to use only one tenth of the number of samples previously needed to compensate for the error induced by inaccurate modelling of optical properties while ensuring the quality of reconstruction,which greatly improved the efficiency of BAE method.In summary,this thesis developed methods to incorporate structural prior into the forward problem of FMT and to incorporate sparsity prior into the inverse problem of FMT,and set up a way to compensate for the error induced by inaccurate modelling of optical properties.The goals of restraining artifacts in FMT reconstruction images and enhancing the accuracy of reconstruction of fluorophore were achieved.