Improved noise propagation in statistical image reconstruction with resolution modeling

Positron emission tomography (PET), like other imaging modalities, has resolution limitations. Two general/common approaches to improve reconstructed image resolution include: (i) the de-convolution scheme, and (ii) system matrix modeling (in statistical image reconstruction methods). An interesting observation about (ii) is that it is able to improve both resolution and noise characteristics of the reconstructed images (unlike (i) which offers a trade-off). In this work, we have used the unified noise model developed by Qi (2003) to perform image covariance calculations without and with the inclusion of resolution modeling in the system matrix of the EM algorithm. We have in particular shown that, while system matrix modeling of finite resolution effects improves the image resolution by direct contribution to the reconstruction task, it is at the same time able to lower the reconstructed image noise due to a compression/widening effect in inter-voxel correlations. We have also experimentally verified this effect.