Regularization-based Reconstruction For Dynamic Fluorescence Molecular Tomography(DFMT)using Spatial And Temporal Correlation

Dynamic fluorescence molecular tomography(DFMT)is a promising optical imaging technique.Compared with conventional static FMT imaging technique,DFMT has the ability to tomographically capture the metabolic process of fluorophore in small animals,and thus can provide richer information for physiological and pathological studies.However,DFMT suffers from low spatial resolution due to its ill-posed nature and the diffuse light,which further reduces the image quality.To overcome the above challenges,we made full use of the sparsity and structural information of fluorescent probe and employed effective algorithms.The work in the paper can be summarized as follows:(1)To improve the quality of FMT images,we utilized the sparsity of fluorophore as prior information.Least absolute and Selection Operator(LASSO)regularization method is applied which introduce L1 regularization term to reduce the modeling error and overcome the ill-posed problem.Alternating Direction Method of Multipliers(ADMM)can be viewed as a framework of convex optimization.It takes the form of a decomposition-coordination procedure,in which the solutions to small local sub-problems are coordinated to find a solution to a large global problem.Thus,we introduce ADMM to solve the FMT inverse model.The results of numerical simulation using mouse CT atlas reveals the effectiveness of the algorithm that it can achieve accurate localization of the fluorescent target.(2)In order to utilize the structural information of fluorophore to improve the quality of reconstruction results,we proposed KNN regularization matrix and Gaussian weighted Laplacian matrix,which assumes that the variance of bioluminescence source energy between any two voxels decreases with the increasing of their spatial distance.The numerical simulation demonstrates that the regularization matrix we proposed,especially the Gaussian weighted Laplacian matrix,leads to significant improvements of the reconstruction quality in both position and form.(3)DFMT reconstruction can be regarded as a sequence of FMT images of a time-varying target.Combined with pharmacokinetic studies,we set a series of spherical targets with different concentrations and sizes to simulate the metabolic process.Numerical simulation is implemented to validate the performance of ADMM and sparse prior strategy.Reconstruction results reveal the reliability and feasibility of ADMM that it is robust to different fluorescent targets.Significant improvements can be obtained with the sparse prior strategy compared with the reconstruction method without structural prior information.In conclusion,the algorithm and strategy we proposed show better reconstruction quality in the numerical simulation,which proves its potential application value in DFMT reconstruction.