When Fast Fourier Transform Meets Transformer for Image Restoration (2024)

Relatedly, Marcin Wichary wrote a nice post about using FFT to remove moiré and halftone effects when scanning images that were printed with halftones.

It's from 2021: Moiré no More (https://newsletter.shifthappens.site/archive/moire-no-more/).

There have been some interesting advances in trying to add spectral information to the data that a learning architecture has at its disposal, but there are a couple roadblocks that I don’t think have been solved yet.

1. Complex-valued NNs are not an easy generalization of real ones.

2. A localization in one domain implies non-local behavior in the other (this is the Fourier uncertainty principle).

Fourier Neural Operators (FNOs) come close to what I want to see in this area but since they enforce sparsity in the spectral domain their application is necessarily limited.

See also: CosAE: Learnable Fourier Series for Image Restoration (2024)

https://sifeiliu.net/CosAE-page/

Was there a conclusion?

[2024]