Penalised least squares image reconstruction from backprojection space for 3D PET

Image reconstruction directly from backprojected images has two advantages over projection-data based reconstruction for 3D PET: i) 3D backprojected images offer data compression compared to large 4D projection data sets and ii) full spatial sampling accuracy of the scanner is retained (unlike with projection-data mashing). This second advantage can be useful for scanners with large numbers of possible lines of response (LORs), as a backprojected image preserves all the positional accuracy of the LORs (which can otherwise be compromised by binning into projections). This work presents an algorithm for penalised least squares (PLS) reconstruction directly from 3D backprojected images. All the data can be used, and the shift-variant 3D point response function of the scanner can be directly accounted for. The proposed algorithm was compared with the ISRA and BPF reconstruction algorithms, and was found to converge significantly more quickly than ISRA and to offer some improvements in noise-contrast behaviour in cold regions when compared to BPF