A number of problems in image reconstruction and image processing can be
addressed, in principle, using the sinc kernel. Since the sinc kernel decays slowly,
however, it is generally avoided in favor of some more local but less precise
choice. In this paper, we describe the fast sinc transform, an algorithm which
computes the convolution of arbitrarily spaced data with the sinc kernel in
operations,
where
denotes the number of data points. We briefly discuss its application to the
construction of optimal density compensation weights for Fourier reconstruction and
to the iterative approximation of the pseudoinverse of the signal equation in
MRI.
Keywords
sinc interpolation, fast transform, nonuniform fast Fourier
transform, density compensation weights, iterative methods,
Fourier analysis, image reconstruction, magnetic resonance
imaging (MRI)