Cross-Reference Maximum Likelihood Estimates for Positron Emission Tomography

Maximum likelihood estimate (MLE) is a widely-used approach for PET image reconstruction. However, it has been shown that reconstructing emission tomography based on MLE without regularization would result in noise and edge artifacts. In the attempt to regularize the maximum likelihood estimate , in this paper, we propose a new and eecient method to incorporate the correlated but possibly incomplete structure information which may be derived from expertise, PET systems or other imaging modalities. A mean estimate smoothing the MLE locally within each region of interest is derived according to the boundaries provided by the structure information. Since the boundaries may not be correct, a penalized MLE using the mean estimate is sought. The resulting reconstruction is called a cross-reference maximum likelihood estimate (CRMLE). The CRMLE can be obtained through a modiied EM algorithm, which is computation and storage eecient. By borrowing the strength from the correct portion of boundary information, the CRMLE is able to extract the useful information to improve reconstruction for diierent kinds of incomplete and incorrect boundaries in Monte Carlo studies. The proposed CRMLE algorithm not only reduces the estimation errors, but also preserves the correct boundaries. The penalty parameters can be selected through human interactions or automatically data-driven methods, such as the generalized cross validation method.