Favor: a fast reconstruction algorithm for volume imaging in PET

A novel 3-D reconstruction algorithm for volume imaging in positron emission tomography (PET) is presented. This algorithm obviates the need to forward-project the data which have not been measured due to the finite length of the scanner. This results in a significant improvement in the reconstruction speed with respect to the algorithm of N.J. Pelc (1979) and P.E. Kinahan and J.G. Rogers (1990). The partially measured oblique projections are filtered with a 1-D ramp filter, whereas the untruncated direct projections are filtered with a 2-D filter, the Favor filter, calculated to ensure an exact reconstruction. A simpler, approximate, version of this algorithm is also discussed in which all projections are filtered with a 1-D ramp function. These two algorithms have been implemented, and data from a volume PET scanner are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>