EM Reconstruction Algorithm with Resolution Modeling applied to an RPC-PET prototype

Abstract

Our group is developing a very high resolution positron emission tomography (PET) prototype based on RPCs (resistive plate chambers). In this work, we implemented a method for iterative image reconstruction using the expectation maximization (EM) algorithm, but using a factorization of the system matrix, in order to include resolution modeling. The system matrix is thus the product of a simple geometric matrix and a convolution matrix, modeling finite resolution effects. The multiplication of the latter by an image is equivalent to performing a convolution in image-space by a shift-invariant symmetric kernel. This method is compared with the standard filtered backprojection (FBP) algorithm and with the EM algorithm without resolution modeling (standard EM). Tests were performed with point source data measured in the RPC-PET prototype and with synthesized data. Results indicate that the EM algorithm with resolution modeling performs better than its analytical counterpart and the standard EM algorithm, with an improvement of more than 25% in image spatial resolution for two point sources, achieving under 0.4 mm FWHM. In simulations with other object geometries, the images obtained with resolution modeling had the lowest noise levels.