A generalized Hann window for apodization of filtered backprojection PET images

In filtered backprojection reconstruction, including the final reconstruction step of the Kinahan and Rogers reprojection algorithm for 3D PET, apodizing windows are used to control the balance between resolution and noise in the output image. Generally, the desire is to use as little apodization as possible, to preserve image resolution, while achieving an acceptable noise level in the reconstructed image. In many circumstances, a Hann window with a cutoff at or below the Nyquist frequency is used with excellent results. The Hann window is continuous in magnitude and slope at its frequency cutoff, which reduces Gibbs ringing in the filtered projections. In some cases the data statistics are sufficient to accept an apodizing function sharper than the Hann window, but are insufficient to permit unapodized reconstruction. Many filter options, such as a rectangular window, have discontinuities in either their magnitude or slope, and therefore do not produce optimal image results. This work presents the design of a Hann window modified by a power transformation of the frequency axis. By adjusting the exponent of the power transformation, the new window can be adjusted continuously between a traditional Hann window cutoff at the Nyquist frequency and a unity function (i.e., no apodization)