EM algorithm system modeling by image-space techniques for PET reconstruction

Methodology for PET system modeling using image-space techniques in the expectation maximization (EM) algorithm is presented. The approach, applicable to both list-mode data and projection data, 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). A basic version of the proposed technique can be implemented using image-space convolution, in order to include resolution effects into the system matrix, so that the EM algorithm gradually recovers the modeled resolution with each update. The improved system modeling (achieved by inclusion of two convolutions per iteration) 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 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 ¹²⁴I (which has a low positron yield and a large positron range, usually resulting in noisier and poorer resolution images) are particularly noticeable.