Bayesian image reconstruction for emission and transmission tomography.

摘要

In nuclear medicine, an estimate of the three-dimensional spatial distribution of injected radionuclide is needed for diagnosis. This estimate is obtained through a reconstruction algorithm. It is a statistical reconstruction since data are noisy. Statistical Bayesian image reconstructions are capable of incorporating accurate system models and including a penalty (prior) to capture the known characteristics of the underlying object. One type of such a prior is the pointwise, independent gamma prior. The independent gamma prior has many nice mathematical properties, but due to the difficulty of finding its parameters at each pixel, it was largely abandoned. In this thesis, we introduce a Bayesian image reconstruction method that uses a novel pointwise prior in the form of a mixture of gamma distributions. We use the mixture model as means of calculating the parameters of the independent gamma prior. We propose a joint-MAP (maximum a posteriori) approach in the form of an iterative algorithm that alternates between a conventional MAP reconstruction and a mixture decomposition, and automatically determines these parameters. First, we apply this joint-MAP approach to transmission tomography. We compare our proposed approach with other transmission reconstruction methods, including filtered backprojection (FBP), and segmented attenuation correction (SAC), in the context of detecting a low-contrast tumor in an attenuation-corrected PET emission reconstruction. The performance results show that our joint-MAP approach outperforms FBP and SAC, especially in the low-count case. We further apply the joint-MAP approach with gamma mixtures to the emission reconstruction problem, and use a MAP-EM algorithm for the reconstruction part. However, the results are not as promising as in the transmission case.