Theory Of Three-dimensional Positron Emission Tomography And

Image reconstruction from projections is a very hot research area all over the world. Analytic image reconstruction technology has simple formula, short reconstruction time and is easy to implement using hardware, so it is widely used in clinic. With the continuously developing of computer technology, the cost of the computation declines rapidly, image quality replaced algorithm speed as No 1 consideration for the usability of a reconstruction technology. Iteration reconstruction technology attracts more and more attentions because of its better image quality. A number of single-object image reconstruction algorithms have been developed, including Least-Squares, Maximum Entropy, Minimum Cross Entropy, Maximum Likelihood and Maximum Posterior, which utilizes statistical model of PET. Some researchers dedicated to find new objects to improve image quality, while others focused on fast implementation of those algorithms, such as Order-subset and various parallel implementations. Professor Wang Yuanmei created a new direction of image reconstruction by utilizing multi-object optimization theory. According to his theory, the question of image reconstruction is to find a noninferior solution for multi-objects. Multi-object image reconstruction theory provide solid base to develop new image reconstruction algorithm. Unlike X-ray CT, PET run in 3D mode naturally. Photons move in 3D direction, and detection system also run in 3D mode to get better sensitivity. It is widely recognized that 3D projection data is vital to reconstruct high quality PET image. One method to utilize 3D projection data is to rebin 3D data into 2D mode; so traditional image reconstruction technology can be used. Rebin process will bring noise which will degrade the image quality. The principle of this paper is to study vector ptimization based image reconstruction technology of 3D PET. In the first chapter, we introduced physical fundamental and detector geometry of 3D PET. Then we gave a mathematical model. In the second chapter, we discussed in detail the principle and common format of the single-object iteration approach. We also gave some common algorithms. In the third chapter, we discussed the theory and implementation of the Vector-Optimization based Image Reconstruction. First, we introduced the theory of vector optimization and approach to get noninferior solution. Then we rewrite equation of image reconstruction into the typical format of a vector optimization problem. Based on this equation, we developed some new image reconstruction algorithms. In chapter four, we simulated 10 algorithms using 3D Hoffman and Utah modal. The result showed that Vector-Optimization based Image Reconstruction technology has better image quality.