PET Image Reconstruction Based On State Space Theory

Positron emission tomography(PET) is a vivo functional imaging, which can access an image reflecting the situation of human metabolism, by photon-pairs detection, data processing and image reconstruction and it has been widely used in the fields like clinical examination, evaluation of efficacy, drug development and biological science research.In order to satisfy the higher and higher quality requirements for the PET imaging, reconstruction methods as a key technology of PET imaging reconstruction is also constantly improved. The thesis takes the problems like inaccurate reconstruction model, slow speed of reconstruction into consideration and proposed the corresponding solution in the state space reconstruction system. The main work this thesis is as follows:Firstly, PET reconstruction quality heavily depends on the accuracy of the measurement model, while the exciting PET reconstruction method for noise processing is too rigidly and too simple, so that it is difficult to describing the PET projection noise. A reconstruction method based on constrained filter is proposed to solve that problem. By taking PET imaging principle and the projection data acquisition process into account, a mixed noise model is built to make full use of noise information. The method provides a better reconstructed results when one obtains only some information on noises but does not know whether the statistics matches the noise level well in advance. The conclusion is also supported by the numerical experiments.Secondly, the PET projection matrix is influenced by too many complex physical factors to obtain the accurate projection matrix. The thesis considers the case that the PET system model is subject to uncertainties and proposes an optimal linear stochastic filtering for PET reconstruction. The method models the uncertainty of the projection matrix as a multiplicative noise, which is addressed as a disturbance for the projection matrix in image reconstruction. It pursues a optimal linear reconstruction in the linear minimum mean-square error sense. Compared to Kalman filter, the approach reconstructs the PET image effectively, whose performance is evaluated with the Shepp-Logan Digital phantom and the computer-synthesized Zubal-thorax-phantom.Thirdly, the thesis considers the problem that iteration methods take long time when reconstructs PET image and proposes a reconstruction method based on the information filtering. This method makes use of the special structure of the PET observation model and maps state variables from state space to the information space, uses the information vectors and the information matrix for iteration. It can guarantee the accuracy as well as reducing the amount of calculation in the process of iteration.At last, a summarization is given, and the problems to be solved in the future are prospected.