I've been dabbling in using Fourier analysis in deep learning lately, and I'm surprised it that I haven't turned up very much research in this area (Fourier Neural Operators being what seems to be the biggest exception). Fourier analysis is such a ubiquitous tool, intuitively I'd think it would work great for deep learning. My suspicion has been that complex numbers are difficult to work with, and maybe I'm just bad at surfacing the relevant research, but I'd be interested to hear from those better informed. (My naive approach has been to simply concatenate the real and complex components together into an n+1 dimensional tensor, but surely there's a way that better respects the structure of complex numbers.)
Limited intuitive interpretability of phase likely restricts the broader use of discrete Fourier transforms in machine learning. Frequency, time, and amplitude are tangible and intuitive concepts, whereas phase often feels awkward and less accessible. Using a power spectrum is common practice, but it comes at the cost of losing precision.
I don't know why but I get this uncanny feeling when looking at the restored images. Maybe it's because I know it is restored, I wonder if I'd feel the same way if I find it in the wilds.
Wait, all my eye-rolling at the TV/film trope of "Computer, Enhance!" de-blurring is now redundant, and that stuff is real?!
This looks incredibly impressive as a result, but I'm wary of the use of metrics like FID to evaluate performance. I can take a high-res image, downsample it, then use the method and measure performance very easily: what percentage of pixels were correctly restored? Instead they're using metrics like FID which - while useful for purely generative techniques - seem a little vague for this purpose.
Might be useful to use gabor filters as the basis function, since just 2d cosine filters doesn't produce particularly sparse output for angled features. The additional overcompleteness would probably be helpful for the NN learning.
A fun little bit of trivia: Mammalian brains implement Gabor filters in the primary visual cortex (V1), as the first step of the visual processing pipeline.
Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc-
tions to faithfully reproduce the main experimental results, as described in supplemental
material?
Answer: [No]
Justification: Although we have answered “No” for now, we intend to release the code and
models to enable the reproducibility of our main experimental results, pending approval
from the legal department. This temporary status reflects our commitment to open access
once all necessary permissions are secured.
There's also 2D rope for ViT, but I don't know how it works exactly.
This looks incredibly impressive as a result, but I'm wary of the use of metrics like FID to evaluate performance. I can take a high-res image, downsample it, then use the method and measure performance very easily: what percentage of pixels were correctly restored? Instead they're using metrics like FID which - while useful for purely generative techniques - seem a little vague for this purpose.