A new 3D backprojection and filtering method for PET using all detected events

The authors have developed a new 3D reconstruction method for positron emission tomography (PET) based on the backprojection and filtering (BPF) technique. It was developed for a rotating large-area detector PET scanner. By starting with event-by-event backprojection rather than histogramming into projections, the positional information from the scanner is fully utilized. Also the data are condensed into 3D image format, rather than 4D format as required by projection based methods. The authors' new method-Atrax-is based on a combination of analytic and algebraic techniques, eliminating the requirement of a shift-invariant point spread function (PSF). All the detected events are used and there is no restriction on the field of view. The key to the method is factorization of the deconvolution step into an axial and a transaxial part. A preliminary 2D reconstruction is used for the calculation of the axial PSF. The axial deconvolution is performed with an iterative method, and the transaxial deconvolution is done in Fourier space. Atrax can produce images with lower noise than standard BPF due to the incorporation of more events, and with improved resolution as compared to projection based methods due to full utilization of the positional information.