Image Reconstruction For Positron Emission Tomography

Positron emission tomography (PET) acts as one of representative techniques of modern nuclear science playing an important role in clinical diagnosis. It provides tissue functional imaging with the aid of radioisotope, which currently makes it one of noninvasion medical imaging tools observing dynamically and quantitatively the physiological and biochemical changes in vivo.The main purpose of this dissertation aims at the methodology of PET image reconstruction which serves as a critical preprocessing step that approaches the unknown image or distribution of radioactivity by using the observed photon counts generated during the progress of scanning. In this dissertation, several novel PET reconstruction methods are introduced: the new space alternating generalized expectation maximization (SAGE) algorithm using variable index set and its application to the nonstationary Gaussian observation model for PET imaging; the multiscale wavelet-based iterative MAP reconstruction algorithm; the reconstruction methods using the sequential WLS (weighted least squares) and the state-spaced based Kalman filtering technique; and finally, the orthogonal moment-based image reconstruction for the limited-angle tomography.Statistical iterative reconstruction methods, particularly those with fast convergent rate, are increasingly important in PET image reconstruction. In this dissertation, the maximum likelihood (ML) estimate for one kind of nonstationary Gaussian observation model is first studied. The model optimization is conducted by the using of the SAGE algorithm. For the reduction of computational time cost, the variable index set technique is further suggested, which also makes full use of the a priori underlying physiological information of PET images. The feasibility and efficiency of the proposed method are verified experimentally in comparison with other commonly used ML estimate methods.Due to the stabilization of the ML estimate, the MAP estimate is introduced accordingly. Conventional MAP algorithm controls the noise behavior by introducing the so-called image a priori information. Such priori plays the role as a smoothness constraint that penalizes the roughness of image estimate and then removes the noisy degradations. Instead of seeking a MAP estimate in image domain, this dissertation considers an efficient alternative within the domain of wavelet. The presented method utilizes a two-step algorithm as follows: 1) the determination of image wavelet coefficients from the observed projection data, and 2) image reconstruction via the wavelet inversion. Moreover, a novel SAGE based optimization...