Research On The Forward And Inverse Problems Of BLT Based On Wavelet Finite Element And Moment Searching

With the development of medicine and pharmacy, the imaging technology in cell and molecular is needed, which makes the molecular imaging developed. Bioluminescent Tomography (BLT), one of the molecular imaging technologies, has attracted more and more attention. Both the forward and inverse problems of the BLT, the aims of which are to obtain the fluence distribution and the source distribution respectively, are studied in this paper.The forward problem of BLT based on non-truncated wavelet finite element is studied first. However, traditional wavelet finite element based on which the non-truncated wavelet finite element is developed is constrained to the problems of regular shape. The non-truncated wavelet finite element method using linear combination of non-truncated wavelet functions across the elements to approximate unknown function is used in the BLT forward problem of 3-D successfully. Theoretical analysis and numerical simulations show that the accuracy of the computation results by the new algorithm are almost as good as the results by finite element method (FEM) while the number of elements and computational complexity greatly reduce compared with FEM.To reduce the ill-posedness in the inverse problem of BLT, a Moment Searching algorithm is developed in this paper. This algorithm uses the moment concept for reference and the source's position receives the feedback through the algorithm of barycenter searching, which makes full use of the 4-D information of the flux density on surface. The position is modified in every iterative step and will converge to the real source's value theoretically. The simulation results show the effectiveness of the algorithm.