Three-dimensional image reconstruction for PET by multi-slice rebinning and axial image filtering

A fast method is described for reconstructing volume images from three-dimensional (3D) coincidence data in positron emission tomography (PET). The reconstruction method makes use of all coincidence data acquired by high-sensitivity PET systems that do not have inter-slice absorbers (septa) to restrict the axial acceptance angle. The reconstruction method requires only a small amount of storage and computation, making it well suited for dynamic and whole-body studies. The method consists of three steps: (i) rebinning of coincidence data into a stack of 2D sinograms; (ii) slice-by-slice reconstruction of the sinogram associated with each slice to produce a preliminary 3D image having strong blurring in the axial (z) direction, but with different blurring at different z positions; and (iii) spatially variant filtering of the 3D image in the axial direction (i.e. 1D filtering in z for each x-y column) to produce the final image. The first step involves a new form of the rebinning operation in which multiple sinograms are incremented for each oblique coincidence line (multi-slice rebinning). The axial filtering step is formulated and implemented using the singular value decomposition (SVD). The method has been applied successfully to simulated data and to measured data for different kinds of phantom (multiple point sources, multiple discs, a cylinder with cold spheres, and a 3D brain phantom).