Sparsity Regularized PET Image Reconstruction

PET has been widely used for imaging 2D or 3D tomography of radioisotope distribution within the patient. But due to the high level noise of the measurement, accurate estimation of isotope distribution is still a challenging issue. During the early development of PET, researches developed the filtered back-projection (FBP) model based on Radon transform for reconstructing PET images. However, FBP method disregards the spatially-variant system response of PET, and statistical noise is neglected and often treated in a post-hoc manner. Hence the accuracy of FBP method is severely limited.On the other hand, assuming data is Poisson distributed, iterative statistical reconstruction algorithms are able to model the physical detection process, and thus have been the primary focus of many recent efforts. However, from the perspective of statistical inference, such high dimensional maximum likelihood estimators are inevitably ill-conditioning. While the anatomical modalities have superior resolution to PET, accurate estimates of anatomical boundaries can be formed from them to influence the PET reconstruction. However such anatomy based PET reconstruction methods rely heavily on the accuracy of image registration of PET and anatomical images like computed tomography (CT) and magnetic resonance imaging (MRI). Moreover, in some studies, the findings of anatomical and functional imaging modalities may disagree, and in some circumstances anatomical imaging modalities might miss some regions that appear suspicious on PET images.In this thesis, a novel algorithm that combines a maximum likelihood function and sparsity penalty is proposed. The resulting model is capable of representing the measured data with Poisson statistics, while the sparsity penalty term in the objective function encourages the reconstructed image patches being sparsely represented by the dictionary. An iterative procedure is then provided to optimize the resulting objective function. To demonstrate the applicability of the novel method, we have tested the proposed algorithm in terms of reconstruction accuracy and detectability based on Monte-Carlo generated data and real patient data.