On Fluorophore Imaging by Diffusion Equation Model:Decompositions and Optimizations  

作　　者：Li-yan WANG Ji-jun LIU 

机构地区：[1]School of Mathematics,S.T.Yau Center of Southeast University,Southeast University,Nanjing 210096,China

出　　处：《Acta Mathematicae Applicatae Sinica》2020年第1期203-222,共20页应用数学学报（英文版）

基　　金：supported by National Science Foundation of China(Nos.11601079,11971104,11531005);the National Science Foundation of Jiangsu Province(BK20150592)。

摘　　要：Fluorescence imaging is a target-specific molecular imaging technology using absorption coefficient of fluorophore.For this imaging model governed by an inverse problem for the coupled diffusion system,which describes the interaction of the excitation field from several boundary sources and the corresponding emission field,we reformulate it as an optimization problem.For solving this non-quadratic optimizing problem,we propose a decomposition scheme,which extracts the horizontal information of the target from the boundary measurement data directly.The realizability of this hybrid imaging scheme is rigorously proved mathematically for cubic and ellipsoid targets,by constructing an indicator function for the horizontal location of the target explicitly.Then based on this horizonal location as a good initial guess for the iteration process,the cost functional is optimized efficiently using the trust domain scheme.Numerical implementations are provided to show the validity of the proposed scheme.

关 键 词：FLUORESCENCE IMAGING diffusion equation INVERSE problem decomposition optimization NUMERICS 

分 类 号：O657.3[理学—分析化学] O439[理学—化学]