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This is incorrect. The frequency domain inverse of the Gaussian ends up yielding a division by zero. There is no inverse for the Gaussian.
by ipv6ipv4 4y ago
This is incorrect. The frequency domain inverse of the Gaussian ends up yielding a division by zero. There is no inverse for the Gaussian.
- colanderman 4y agoThat is mathematically true but not practically. Though indeed the Gaussian kernel has lots of zeros [1], in actuality, (a) the zeros themselves are at points, not regions, and therefore of little consequence, and (b) in practice the noise generated from reamplifying frequencies near these zeros can be minimized via techniques such as Wiener deconvolution [2]. [1] https://en.wikipedia.org/wiki/Window_function#Gaussian_window https://en.wikipedia.org/wiki/Window_function#Gaussian_windo... [2] https://en.wikipedia.org/wiki/Wiener_deconvolution https://en.wikipedia.org/wiki/Wiener_deconvolution
- godelski 4y agoThey didn't claim invertible. The de-gaussinization is a reversible process albeit not invertible. I actually say more in this comment https://news.ycombinator.com/item?id=35111998 https://news.ycombinator.com/item?id=35111998