Investigation Of Positron Emission Tomography Image Statistical Reconstruction

PET(Positron Emission Tomography)is one of the most advanced techniques in the world. It joins the latest advantage of the nuclear physics, computer vision, molecular biology, medical images, and it is one of noninvasive medical imaging tools observing dynamically and quantitatively the physiological and biochemical changes in vivo. Mathematical methods are performed on the sinogram to recover the activity map, which indicates the metabolic changes of the organs.PET image reconstruction algorithms available are introduced in the first part of the thesis. Currently, it can be classified into analytical and iterative method. The analytical methods are simplicity and fastness. However, its reconstructed images are very noisy. Though the famous maximum-likelihood expectation-maximization(MLEM) can better express system models of physical effects and modeling the statistical Poisson character of the data, the reconstructed images always start deteriorating to produce"checkerboard effect"as the iteration proceeds and it suffers slow convergence. The popular Bayesian reconstruction can greatly improve reconstruction by incorporating image prior information. But it always find that, heavily relied on the information within a limited neighborhood, conventional Bayesian methods can only contribute limit local prior information to reconstruction, which may leads to unfavorable oversmoothing effect or bring staircase edge artifact to reconstruction. To improve the shortage of the iterative method, we do the following work on PET reconstruction algorithms:The traditional Least-Squares reconstruction algorithms of positron emission tomography can not effectively suppress the noise and have slow convergence. In order to solve the problem, we introduce a penalty prior term into the least-squares algorithm, and combine with Ordered Subsets (OS) method, forming the penalized least-squares algorithm, which can reconstruct a higher quality image, but also enhance the convergence preferable.With the Thin Plate prior in the Bayesian reconstruction, combining the anisotropic diffusion filter with a better diffusivity, we have a new reconstruction algorithm which can not only protect the edge of the image as the Thin Plate, but also get the adaptive effort like the back and front diffusivity.We introduce a nonlocal prior as a penalty to the least squares reconstruction algorithms, and combine the anisotropic diffusion filter with a better diffusivity in the interiteration, developing an improved regularized PET image reconstruction algorithm. The results showed that it is useful.