Resampling Images in Fourier Domain
G. M. Bernstein, Daniel Gruen · Publications of the Astronomical Society of the Pacific · 2014
When simulating sky images, one often takes a galaxy image F ( x ) defined by a set of pixelized samples and an interpolation kernel, and then wants to produce a new sampled image representing this galaxy as it would appear with a different point-spread function, a rotation, shearing, or magnification, and/or a different pixel scale. These operations are sometimes only possible, or most efficiently executed, as resamplings of the Fourier transform of the image onto a u -space grid that differs from the one produced by a discrete Fourier transform (DFT) of the samples. In some applications, it is essential that the resampled image be accurate to better than one part in 10 3 , so in this paper, we first use standard Fourier techniques to show that Fourier-domain interpolation with a wrapped sinc function yields the exact value of in terms of the input samples and kernel. This operation scales with image dimension as N 4 and can be prohibitively slow, so we next investigate the errors accrued from approximating the sinc function with a compact kernel. We show that these approximations produce a multiplicative error plus a pair of ghost images (in each dimension) in the simulated image. Standard Lanczos or cubic interpolators, when applied in Fourier domain, produce unacceptable artifacts. We find that errors less than one part in 10 3 can be obtained by (1) fourfold zero-padding of the original image before executing the x → u DFT, followed by (2) resampling to the desired u -grid using a six-point, piecewise-quintic interpolant that we design expressly to minimize the ghosts, then (3) executing the DFT back to x -domain.