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Comment by jjcm | Hacker News Reader

I'm honestly surprised that it took this long for someone to use wavlets as a starting point in the image translation architecture. Frequency separation has been used for ages in the pro-photoshop realm for advanced editing / restyling. It makes sense that you'd get excellent performance with it in a GAN.

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This isn't really wavelets, though I guess it's a related technique. It's using a laplacian pyramid, which as you suggest is doing frequency separation, but it's achieved in the spatial domain by blurring and up/downsampling. (http://www.liralab.it/teaching/SINA_10/papers/burt-adelson19...)

It's far from the first use of this technique for CNNs, even for similar tasks. For example, there's LapGANs, that combined GANs with laplacian pyramids about 5 years ago. There's also LapSRN, that used this representation for superresolution.

This doesn't use wavelets afaics (they are not mentioned in the article), it uses something called 'Laplacian Pyramid'. That can be used separate a signal by frequency but seems to do the whole image at once. Looks to be the good old add-laplacian (ie 'blur') and subtract-from-the-original method (to get remaining high frequency).

I think wavelets usually have a limited extent in space (depending which basis shape you choose I guess).

Maybe they could make use of FFT for this separation, but it's probably hard to beat blur-and subtract for simplicity of implementation.

Essentialy, you do the same thing as an FFT for separation. A gaussian blur is a low-pass filter, and functionally the same as selecting all frequency component within a radius r of the DC component (assuming the DC component is in the center of the image). The radius r depends on the width of the gaussian kernel.

The only difference could be in computational time (might be that the FFT is faster) and will be different if you use a different kind of blurring (i.e. non-gaussian such as selecting a square region in the frequency domain).

Agreed! And in cases where the convolution kernel (bokeh, but in frequency space) is something more complicated than gaussian, FFT can definitely be a very good option (kernel/bokeh-res can be near-ish to the res of the image-to-convolve, for example, and full-colour kernels/bokehs too).

I don't have any quantitative evidence on computational performance of the FFT versus the typical laplacian pyramid technique, but I'd be surprised if FFT is faster. The classical laplacian pyramid -- developed in the 80s -- is really quite simple and fast. http://www.liralab.it/teaching/SINA_10/papers/burt-adelson19...

I found a paper from 2019 in the references of this current paper: https://arxiv.org/abs/1903.09760

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