Cross-Reference Maximum Likelihood Estimates for Positron Emission Tomography

Yuan-Pei Xu, Horng-Shing Lu

Research output: Other contribution


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.
Original languageEnglish
StatePublished - 1995


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