Filtered backprojection reconstruction of combined parallel beam and cone beam SPECT data

The reconstruction problem for a combined parallel beam (PB) and cone beam (CB) imaging geometry has been addressed. The general algorithm (CB-FBP) of Defrise and Clack has been applied to this geometry and shown to provide accurate images as expected. A second algorithm specifically tailored to the PB-CB geometry was developed. It uses the general principles of the CB-FBP method to combine a shift-variant filtering of the PB data with a standard reconstruction of the CB data using the algorithm of Feldkamp, Davis and Kress (FDK). This 'mixed' algorithm has the advantage of fewer interpolation steps, thereby reducing reconstruction time and providing more accurate reconstructions. The algorithms were applied to noiseless data from a computer-generated 3D Shepp phantom. Both the CB-FBP algorithm and the mixed algorithm successfully combine the CB and the PB data to correct the well known artefacts observed when reconstructing CB data acquired with a circular orbit. The mixed algorithm is about twice as fast as CB-FBP and results in better image quality, due to decreased discretization errors. However, the two algorithms yield comparable image quality when applied to a disc phantom measured with a two-headed SPECT system.