Cross-Reference Maximum Likelihood Esimate Positron Emisstron Emission Tomography

Abstract

The random observations of a positron emission tomography （PET）follow a Poisson distribution. The mean is indirectly related to the target image image intensity by a linear transformation. Therefore, there are two sources of errors inherent in the reconstruction of PET images. One is due to the random variation of a Poisson distribution. This can be handled via the maximum likelihood paaroach. The other source of error is caused by the nonuniqueness in inverting the linear transformation. This can be managed by the method of regularization. In order to regularize the maximun likelihood estimate, we propose a new and efficient method to incorporate the correlated but incomplete boundary information. According to the boundary locations,we can have a mean estimate that smooth the maximum likelihood estimate locally with boundaries. Since the boundaries may be incomplete or incorrect,this mean estimate is only a reference point. Introducing a penalty parameter, we can do the fine adjustment between the maximum likelihood and mean estimates. The resulting reconstruction is called a cross-reference maximum likelihood estimate（CRMLE）. The CRMLE can be obtained through the modified EM algorithm. It is computation and storage effcient. With proper penalty parameters, the CRMLE can outperform the maximum likelihood estimate and the other regularized estimates. The penalty parameters can be selected through human interactions or automatically data driven methods, such as the generalized cross validation. For different kinds of incomplete and incorrect boundaries, the CRMLE is able to extract the useful information to improve reconstruction. The Monte Carlo studies show that the CRMLE is practically appealing.