Things to Consider
What was a Gaussian pyramid is now a sinc pyramid.
What was a DoG pyramid is a DoS pyramid, a set of nearly perfect, nearly 'orthogonal' bandpass filters.
Determined the appropriate sinc filter for no-loss filtering, then dilated it to preserve only the frequencies that the downsampled image in each level of the pyramid could represent.
Performed a separable convolution with imfilter.
Note: did try performing this filtering by using a custom kernel with imresize, but there were issues so that line was abandoned.