EM algorithm resolution modeling by image-space convolution for PET reconstruction

A method for modeling and recovering resolution in the expectation maximization (EM) algorithm via two image-space convolutions per iteration is presented. The approach is of particular significance to EM algorithm implementations which otherwise only use basic system models, such as those which calculate the system matrix elements on the fly rather than using pre-calculated values. The first convolution is applied to a copy of the image estimate prior to forward projecting this copy. The second is performed on the backprojected correction image prior to its use to multiplicatively update the original (not convolved) image estimate. The inclusion of resolution-modeling convolution at these two stages corresponds to extending the system transfer matrix, and the EM algorithm gradually recovers the modeled resolution with each update. The approach does not constitute regularization in any way, but rather the improved system modeling results in both enhanced resolution and lower noise, and there is often no need for regularization - other than to limit the number of iterations. Tests have been performed with simulated list-mode data and also with measured phantom and patient projection data from a GE Advance PET scanner, for both [¹⁸F]-FDG and [¹²⁴I]-NaI. The method demonstrates improved image quality in all cases when compared to the conventional FBP and EM methods presently used for clinical data (which do not include resolution modeling). The benefits of this approach for I-124 (which has a low positron yield and a large positron range, usually resulting in noisier and poorer resolution images) are particularly noticeable.