The Research Of PET Image Reconstruction Algorithm Based On Maximum A Posterior

As one of the new imaging technologies applied to clinic since CT(Computed Tomography) and MRI(Magnetic Resonance Imaging), PET(Positron Emission Tomography) has been widely used in tumor cell detection, disease diagnosis in the respect of heart, nervous system and psychiatric diseases as well as new drug development.The purpose of PET imaging is to obtain an intracorporal distribution produced by radioactive substance. Therefore, how to reconstruct a high quality image based on the scan data has always been an important research subject in the field of PET. Generally speaking, the PET image reconstruction algorithms can be divided into two types, the analytic method and the iterative method. Being the representative of the analytic method, the filtered back projection algorithm is on the basis of the central slice theorem and Fourier transform, whose advantages include simple calculation, fast imaging speed, etc. However, many noise in the projection data may cause difficulties in reconstructing the satisfactory image with the analytical method, thus affect the result of clinical diagnosis. The iterative method can be divided into methods of algebraic iterative and statistical iterative. The algebraic iteration method is similar to the analytic one. It is hard to reconstruct images of high-quality by utilizing complex and various physical imaging conditions and statistical models during the process of image reconstruction. That is also the reason why the method is less used in PET image reconstruction. Based upon the statistical model of data observation, the statistical iteration method can reconstruct the high accuracy reconstructed images, which is the most widely used method in PET image reconstruction. There are many classical PET image reconstruction algorithms in the statistical iterative method, such as MLEM(Maximum Likelihood Expectation Maximized), OSEM(Ordered Subset Expectation Maximization), MAP(Maximum A Posterior) etc. The main research subject of this paper is the MAP algorithm that is also known as the PML or Bayesian algorithm.This paper consists of five chapters as follows:In chapter one, we first introduce the background and significance of PET imaging technology, followed by reviewing the history and development of PET image reconstruction algorithm. Finally, the main research content and structure arrangement of this paper are briefly summarized.Covering the basic theory of PET image reconstruction algorithm, the second chapter talks about the advantages and disadvantages of some classical reconstruction algorithms within PET. The rest chapters are the key parts, which contain the results of this research.We propose a new Bayesian image reconstruction algorithm in the third chapter by combining the AMD(Anisotropic Median-Diffusion) filter with the MRP(Median Root Prior) algorithm. Because the median filter has no obvious effect on Gauss and Poisson noise, it is difficult to obtain a satisfactory results with the MRP algorithm. Merging the AMD filter into the MRP algorithm in a new algorithm will effectively suppress all noise in the reconstructed images. The simulation results show that the new algorithm gains a good compromise in two ways: noise suppression and edge protection. Moreover, the quality of the reconstructed images has been greatly improved.We put forward a PET image reconstruction algorithm based upon penalized maximum likelihood by introducing AMD model into PET image reconstruction algorithms in the fourth chapter. The new algorithm can obtain better reconstruction results in the comparison with comparison experiments. In addition, compared with similar algorithms, such as MLEM-PDE, the new algorithm is strongly practicable due to the advantages of AMD model, simple parameter setting, and insensitivity to the gradient threshold values and diffusion number as well.In the fifth chapter, a new PET image reconstruction algorithm based on penalized maximum likelihood by combining the modified TV(Total Variation) model with MLEM algorithm comes into being. The noise within the PET images is mainly Poisson noise, while some traditional PET image reconstruction algorithms, such as MLEM, MRP and MAP etc., have better suppression effect on the general additive noise, but not on Poisson noise. By introducing the PMTV(Poisson-modified Total Variation) model into MLEM algorithm, the new algorithm can effectively suppress Poisson noise in the reconstructed images, and improve the quality of the reconstructed images.