PET Image Reconstruction Based On Information Estimation

Positron Emission Tomography(PET)plays an important role in qualitative diagnosis and metastasis of tumors.Therefore,it is very necessary to improve imaging quality of PET.However,most of the existing reconstruction algorithms rely heavily on the linear model of PET.Given that PET is affected by many physical factors,such as detector efficiency,geometric size of detection system,attenuation of gamma photons by biological tissues and scattering effects,etc.The linear model cannot match the nonlinear relationship between tracer concentration and sinogram.This paper begins with offering a new observation model to characterize the complicated relationship between the tracer concentration and sinogram by introducing an unknown input term,which consists of two parts.One is a coefficient matrix,which further describes the linear part of the projection;the other is an unknown input,which characterizes the nonlinear relationship between the tracer concentration and the sinogram.Based on the new model,the PET image reconstruction is reformulated as a linear,optimal estimation in state-space in the sense of unbiased minimum variance.This paper proposes three new reconstruction algorithms.The first method uses the singular value decomposition method to divide the observation into two parts: the observation containing the unknown input and the observation without the unknown input.A reconstruction method is proposed which discards the bad observation data containing the unknown input,and uses the observations that do not contain unknown input to estimate the concentration distribution of the tracer and reconstruct the PET image.However,due to the discarding of some observations,the quality of the reconstructed images obtained is expected to be further improved.Therefore,thesecond method is proposed to find a reconstruction method with unbiased minimum variance by using all the observation data of PET.Besides,attempts were made to reconstruct the concentration distribution of the unknown input and tracer at the same time.Since the two methods all limit with the unknown input matrix,so the third method is proposed,which starts with introducing a linear and recursive relation with an unknown estimation gain,eliminates the difficulty induced by the unknown input term by projecting sinogram onto the null space of the coefficient matrix of unknown input,and derives the estimation gain by the idea of Kalman filter.Based on this estimation model,a reconstruction algorithm based on unbiased linear optimal estimation is proposed,which has wider application range than the former two methods.Finally,we compare the Maximum Likelihood-Expectation Maximization reconstruction(ML-EM),the Kernel-based Expectation Maximization reconstruction(KEM),the Kalman Filtering reconstruction(KF)with the proposed algorithms by calculating Mean Square Error(MSE)and Signal Noise Rate(SNR)by a simulation experiment.The experiment result shows that the algorithm proposed in the paper enjoys the larger SNR,the smaller MSE as well as the clearer reconstruct image and reconstructs the size and shape of the tumor better than the others.Hence,we come to a conclusion that our algorithms are superior to the others.