PET point spread function modeling and image deblurring using a PET/MRI joint entropy prior

The quantitative accuracy of PET is degraded by partial volume effects caused by the limited spatial resolution capabilities of PET scanners. In this paper, we describe an image de-blurring technique that uses the spatially varying point spread function of the scanner measured in the image space. To stabilize the deconvolution problem, we introduce the joint entropy between the PET image and a high resolution MR image as an information theoretic penalty function. We present a computationally efficient framework for minimizing the resultant cost function. By means of simulations on the Brain-Web phantom, we show that our method leads to faster convergence and a lower mean squared error. We then applied our method to a phantom and a human dataset and demonstrated that, compared to standalone deblurring, which tends to amplify noise, the joint entropy prior leads to a smooth PET image with sharp boundaries consistent with MRI.