Quasi-Monte Carlo Methods In Computed Tomography

Monte Carlo(MC)method,as a powerful simulation tool,has been rapidly applied to radiotherapy,medical imaging and nuclear medicine because it can simulate the underlying physical interactions between the radiation and matter.Quasi-Monte Carlo(QMC)method is a deterministic version of MC method,and the convergence order of QMC method is asymptotically much faster than that of MC for a fixed dimension.As far as we know,so far there have been a large number of methods based on MC to estimate and correct photon scatter signals in computed tomography(CT),but there is no application of QMC in estimating and correcting photon scatter signals in CT.CT has been widely used in many fields such as material sciences,nondestructive testing,medicine,especially in medical diagnosis,and has revolutionized diagnostic radiology with its great advantages of non-destructive,non-overlapping images and highresolution.However,scatter signals and beam hardening produces duck streak,cupping and hardening artifacts and reduces the contrast resolution of the reconstructed CT image.How to quickly estimate and correct the scatter signal and accurately estimate the energy spectrum,so as to eliminate the scattering artifacts and hardening artifacts in CT images,is very important for reconstructing high-quality CT images.The work of this thesis mainly focuses on using QMC to quickly estimate and correct the scatter singal and using QMC for energy spectrum estimation and image reconstruction in CT.First,we transform the path probability of photon as it interacts with a phantom into a high-dimensional integration and propose a new algorithm called gQMCFRD,which combines GPU-based QMC with forced random detection(FRD)to simulate this integral.FRD only considers the photons reaching the detector,which improves the photon utilization rate and reduces the calculation.Compared with MC-GPU,the efficiency improvement factor(EIF)is tens to thousands of times in all cases.Secondly,in order to maximize the photon utilization rate,the gQMCFRD method is extended,a GPU-based QMC and fixed forced detection(FFD)method called gQMCFFD is proposed for estimating and correcting scatter signals.FFD considers all photons that theoretically reach the detector.Compared with FRD,FFD further improves the utilization of photons.It is proved that the derived high-dimensional integral is the solution of the linear Boltzmann transport equation.To understand why QMC is more effective than MC in simulating the scatter signal in CT,the mean dimension of the scatter estimator of several objects is calculated,and it is found that although the formal dimension of the estimator 4n tends to infinity,its mean dimension does not exceed 4.This partialy explains the superiority of the method based on QMC.Finally,the gQMCFFD algorithm is used for the energy spectrum estimation and image reconstruction in CT.The EM with scatter correction(SC)and FDK with SC are proposed.Experimental results show that the proposed method can estimate the energy spectrum more accurately,and basically eliminate the scatter and hardening artifacts of reconstructed CT images.