Abstract: 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.Considering 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,the linear model cannot match the nonlinear relationship between tracer concentration and sinogram.This paper proposed a new observation model to characterize the complicated relationship between the tracer concentration and sinogram by introducing an unknown input term.This term 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 relation ship between the tracer concentration and the sinogram.Based on the new model,the PET image reconstruction is reformulated as a linear unbiased optimal estimation.Then,a linear and recursive relation with an unknown estimation gain is introduced,the difficulty induced by the unknown input term is solved by projecting sinogram onto the null space of the coefficient matrix of unknown input.Based on the design idea of Kalman filter,the estimation gain is derived.Finally,the Expectation-Maximization reconstruction (EM),the Kernel-based EM algorithm (KEM) and the Kalman Filtering method (KF) are compared with the proposed algorithm by calculating Mean Square Error (MSE) and Signal-Noise-Rate (SNR).The experiment results show that the proposed algorithm has larger SNR,smaller MSE as well as more clear reconstruct image,and reconstructs the size and shape of the tumor better than the others.Hence,the proposed algorithm of reconstruction has better quality to the others.

Key words: Kalman filter, Optimal estimation, Unbiased estimation, Unknown input