  The pseudo-polar Fourier transform is a specialized non-equally spaced
Fourier transform, which evaluates the Fourier transform on a near-polar grid,
known as the pseudo-polar grid. The advantage of the pseudo-polar grid over
other non-uniform sampling geometries is that the transformation, which samples
the Fourier transform on the pseudo-polar grid, can be inverted using a fast
and stable algorithm. For other sampling geometries, even if the non-equally
spaced Fourier transform can be inverted, the only known algorithms are
iterative. The convergence speed of these algorithms as well as their accuracy
are difficult to control, as they depend both on the sampling geometry as well
as on the unknown reconstructed object. In this paper, we present a direct
inversion algorithm for the three-dimensional pseudo-polar Fourier transform.
The algorithm is based only on one-dimensional resampling operations, and is
shown to be significantly faster than existing iterative inversion algorithms.
