Minimum Cross-entropy Reconstruction of PET Images with Anatomically Based Anisotropic Median-Diffusion Filtering

We propose a spatially-variant anisotropic median-diffusion filter prior aided by anatomical knowledge for PET reconstruction. The anisotropic median-diffusion filter is applied locally to an anatomical region which is defined from a co-registered CT image. The individually smoothed regions are then combined to form a prior term in the minimum cross-entropy reconstruction algorithm. A simulated PET thorax phantom with lesions was investigated in terms of bias and contrast versus noise tradeoffs. Compared with MLEM and three other maximum a posteriori (MAP)-like reconstruction algorithms, the proposed algorithm demonstrated better bias-noise tradeoff except when the lesion was close to an anatomical boundary and better contrast-noise tradeoff in all cases.