## 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.

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 language | English |
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State | Published - 1995 |