We developed a maximum a posterior (MAP) reconstruction method for positron emission tomography (PET) image reconstruction incorporating magnetic resonance (MR) image information, with the joint entropy between the PET and MR image features serving as the regularization constraint. A non-parametric method was used to estimate the joint probability density of the PET and MR images. Using realistically simulated PET and MR human brain phantoms, the quantitative performance of the proposed algorithm was investigated. Incorporation of the anatomic information via this technique, after parameter optimization, was seen to dramatically improve the noise versus bias tradeoff in every region of interest, compared to the result from using conventional MAP reconstruction. In particular, hot lesions in the FDG PET image, which had no anatomical correspondence in the MR image, also had improved contrast versus noise tradeoff.Corrections were made to figures 3, 4 and 6, and to the second paragraph of section 3.1 on 13 November 2009. The corrected electronic version is identical to the print version.