Investigation Of Positron Emission Tomography Image Reconstruction

PET (Positron Emission Tomography) is one of the most advanced techniques in the world. It could be used to study the metabolism and the function activity of human body in molecular level with the predominant performances in the research fields of oncology, cardiology, neurology and new medicine exploitation. Image reconstruction from projections is very important in designing PET instrumentation. It has become more and more important in PET research with wide application of PET and fast development of computer technology. The thesis is dealt with PET image reconstruction. The imaging of PET is to count the photon events emitted by the annihilation. The purpose of reconstruction is to recover the density distribution of isotopy. In reconstruction practice, we have to discrete density distribution into pixels. The isotopy distribution is uniformly through the whole pixel, and it emits positron follow a space Poisson point process. Due to the linearity of imaging system, the measured values are i. i. d. Poisson distribution.PET image reconstruction algorithms available are introduced in the first part of the thesis. Currently, it can be classified into analytical and iterative method. Filtered back projection is one of the famous analytical methods which are characteristic of simplicity and fastness. However, its reconstructed images are very noisy. Iterative methods can be divided into algebraic iteration and statistical iteration method. The former is based on algebraic equation theory, while the latter is based on kinds of statistical rules, such as minimum least square, maximum likelihood and maximum a posterior. Because of introducing all kinds of physical and statistical models into the image reconstruction, iterative method can produce better images than filtered back projection.Ordered subsets separable paraboloidal surrogate algorithm (OSSPS) is considered as a better PET image reconstruction than classical maximum likelihood expectation maximization (MLEM). However, it lacks repetition because of its requirement for designated relaxation parameters. In this thesis, we developed a new image reconstruction algorithm named as EMIOT by introducing incremental optimization transfer theory into PET combined with replacing original function by a surrogate function. It does not need designated relaxation parameters but also is comparable to OSSPS in image reconstruction.The images reconstructed by median root prior image reconstruction (MRP) are still noisy due to median filter's poor performance in removing Gaussian and Poisson noise. We proposed a new algorithm which combines anisotropic diffusion filter with median filter in PET. The new algorithm is better than traditional MAP and MRP both from subjective and objective perspective.We developed a new PET image reconstruction algorithm named as MLEM-PDE, which is an improved MLEM regularized by interiteration filter. Because anisotropic diffusion filter based on partial differential equation can remove noise in nuclear medicine images, we used it in this thesis. The results showed that it can be used in PET imaging, especially in clinical situation.ROF is an extensive used model in image restoration community, however, it can not be used in PET imaging directly. In this thesis, we considered the statistics in PET projection data and employed edge-preserving prior function, which can modify ROF. From the variational method not expectation maximization method, we get a new good image reconstruction framework. At last, we deduce an accelerated algorithm by introducing a relaxation parameter into MLEM which decrease with iteration.