2.5-D simultaneous multislice reconstruction by series expansion methods from Fourier-rebinned PET data

True three-dimensional (3-D) volume reconstruction from fully 3-D data in p ositron emission tomography (PET) has only a limited clinical use because o f its large computational burden. Fourier rebinning (FORE) of the fully 3-D data into a set of 2-D sinogram data decomposes the 3-D reconstruction pro cess into multiple 2-D reconstructions of decoupled 2-D image slices, thus substantially decreasing the computational burden even in the case when the 2-D reconstructions are performed by an iterative reconstruction algorithm . On the other hand, the approximations involved in the rebinning combined with the decoupling of the image slices cause a certain reduction of image quality, especially when the signal-to-noise ratio of the data is low. We propose a 2.5-D Simultaneous Multislice Reconstruction approach, based o n the series expansion principle, where the volume is represented by the su perposition of 3-D spherically symmetric bell-shaped basis functions. It ta kes advantage of the time reduction due to the use of the FORE (2-D) data, instead of the original fully 3-D data, but at the same time uses a 3-D ite rative reconstruction approach with 3-D basis functions. The same general a pproach can be applied to any reconstruction algorithm belonging to the cla ss of series expansion methods (iterative or noniterative) using 3-D basis functions that span multiple slices, and can be used for any multislice sin ogram or list mode data whether obtained by a special rebinning scheme or a cquired directly by a PET scanner in the 2-D mode using septa. Our studies confirm that the proposed 2.5-D approach provides a considerable improvemen t in reconstruction quality, as compared to the standard 2-D reconstruction approach, while the reconstruction time is of the same order as that of th e 2-D approach and is clinically practical even on a general-purpose comput er.