GaussianMatrix[] supports a Method -> "Bessel" option which the documentation describes (in the Details section) as:

With the default option setting Method->"Bessel", GaussianMatrix[r] has elements proportional to $\prod_{i=1}^2 \text{exp}(-\sigma^2)I_{x_i}(\sigma^2)$, yielding a kernel with optimal discrete convolution properties.

Does anyone have a reference to a paper or other explanation for this kind of window function/kernel design, that explains in which sense this has optimal discrete convolution properties? Basically i want to understand the theory behind it so i can design other kernels in a similar manner.

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    $\begingroup$ Have you seen these two papers by Lindeberg? $\endgroup$ – J. M.'s technical difficulties Mar 15 '19 at 12:47
  • $\begingroup$ @J.M.isslightlypensive Thank you very much! This scale-space theory for discrete signals looks exactly like the hint i was hoping for! I'll dig into the theory of it and then hopefully be able to derive a proper discrete Airy disk kernel with it :) Also i would accept this if you post it as an answer. Thanks again! $\endgroup$ – Thies Heidecke Mar 15 '19 at 13:11
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    $\begingroup$ Maybe later, when I have time to write a good executive summary of Lindeberg's stuff. Alternatively, if you manage to write a summary of those papers, you could answer this question yourself. ;) $\endgroup$ – J. M.'s technical difficulties Mar 15 '19 at 13:18

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