Penalised least squares image reconstruction from backprojection space for3D PET

Image reconstruction directly from backprojected images has two advantages over projection-data based reconstruction for 3D PET: i) 3D backprojected i mages 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 the positional accuracy of the LORs (which can otherwise b e compromised by binning into projections). This work presents an algorithm for penalised least squares (PLS) reconstruction directly from 3D backproj ected images. All the data can be used, and the shift-variant 3D point resp onse function of the scanner can be accounted for. The proposed algorithm w as compared with the ISRA and BPF reconstruction algorithms, and was found to converge significantly more quickly than ISRA and to offer some improvem ents in noise-contrast behaviour in cold regions when compared to BPF. Howe ver, with current computational limitations, the algorithm can only practic ally be applied to images up to a maximum size of 64x64x64 voxels.