GaussianMatrix algorithm details

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.

• Have you seen these two papers by Lindeberg? – J. M. is in limbo Mar 15 '19 at 12:47
• @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! – Thies Heidecke Mar 15 '19 at 13:11
• 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. ;) – J. M. is in limbo Mar 15 '19 at 13:18