A theoretical study of the contrast recovery and variance of MAP reconstructions from PET data

We examine the spatial resolution and variance properties of PET images reconstructed using maximum a posteriori (MAP) or penalized-likelihood methods. Resolution is characterized by the contrast recovery coefficient (CRC) of the local impulse response. Simplified approximate expressions are derived for the local impulse response CRC's and variances for each voxel. Using these results we propose a practical scheme for selecting spatially variant smoothing parameters to optimize lesion detectability through maximization of the local CRC-to-noise ratio in the reconstructed image.