A Mexican Hat with holes: calculating low resolution power spectra from
  data with gaps
  A simple method for calculating a low-resolution power spectrum from data
with gaps is described. The method is a modification of the $\Delta$-variance
method previously described by Stutzki and Ossenkopf. A Mexican Hat filter is
used to single out fluctuations at a given spatial scale and the variance of
the convolved image is calculated. The gaps in the image, defined by the mask,
are corrected for by representing the Mexican Hat filter as a difference
between two Gaussian filters with slightly different widths, convolving the
image and mask with these filters and dividing the results before calculating
the final filtered image. This method cleanly compensates for data gaps even if
these have complicated shapes and cover a significant fraction of the data. The
method was developed to deal with problematic 2D images, where irregular
detector edges and masking of contaminating sources compromise the power
spectrum estimates, but it can also be straightforwardly applied to 1D timing
analysis or 3D data cubes from numerical simulations.
