Exact rebinning methods for 3D PET

The high computational cost of data processing in volume PET imaging is still hindering the routine application of this successful technique, especially in the case of dynamic studies. This paper describes two new algorithms based on an exact rebinning equation, which can be applied to accelerate the processing of 3D PET data. The first algorithm, FOREPROJ, is a fast forward projection algorithm which allows, for example, to calculate 3D attenuation correction factors (ACFs) directly from a 2D transmission scan, without reconstructing the attenuation map as in the standard procedure. The use of FOREPROJ speeds up the estimation of the 3D ACFs by more than a factor 5. The second algorithm, FOREX, is a new rebinning algorithm which is also more than 5 times faster than the standard method (the reprojection algorithm, 3DRP), without suffering from the image distortions generated by the approximate Fourier rebinning (FORE) at large axial apertures. Both algorithms have been implemented and applied to data simulated for a scanner with a large axial aperture (30°), and also to data acquired with the ECAT HR and the ECAT HR+ scanners. Results demonstrate the important speed-up and the excellent accuracy achieved by these algorithms