An exact Fourier rebinning algorithm for 3D PET imaging using panel detectors

Abstract We present an exact Fourier-based algorithm for rebinning 3D data generated by a stationary dual-panel PET system to obtain direct slices for subsequent slice-by-slice reconstruction. The algorithm is computationally efficient and can greatly reduce the problem dimensionality and computation complexity of the reconstruction task. By conducting computer simulation studies in which the effects of scatter, randoms, detector response functions and attenuation correction are not considered, we demonstrate that direct slices generated by the proposed algorithm are quantitatively accurate and exhibit substantially better noise characteristics than the original direct slices. However, image artefacts, occurring at axial intensity discontinuities and in regions close to the axial axis, can be observed. With preliminary supporting evidence, we stipulate that these artefacts are due to errors in discrete implementations of partial derivatives of the 3D data. Although general weightings can be used in the proposed rebinning algorithm, in this work we only study the use of uniform weightings and the resulting direct slices exhibit non-uniform noise distributions, with the central slices being less noisy. In future studies, by using general weightings to reduce contributions of the data that are acquired at large oblique angles, we expect that more uniform noise distributions can be achieved, and axial blurring due to parallax errors can be reduced, at the cost of overall image variance.