Anatomy assisted MAP-EM PET image reconstruction incorporating joint entropies of wavelet subband image pairs

A promising approach in PET image reconstruction is to incorporate high resolution anatomical information (measured from MR or CT) taking the anato-functional mutual information (MI) or its joint entropy (JE) as the prior. The MI or JE of the images only classify voxels based on intensity, while neglecting structural spatial information. In this work, we have implemented an anatomy assisted MAP-EM algorithm wherein the JE measure is supplied by spatial information generated using wavelet analysis. This approach has the benefit of utilizing some theoretical advantages of wavelets, including the ability to decompose an image of certain size into downsampled subbands. The proposed MAP-EM algorithm involves calculation of derivatives of the subband JE measures with respect to PET image intensities, which we have shown can be computed very similar to how inverse wavelet transform is performed. Using simulations of a mathematical human brain phantom with activities generated based on a clinical FDG study, it was observed that compared to conventional EM reconstruction, the proposed MAP-EM algorithm exhibited improved quantitative performance.