When Fast Fourier Transform Meets Transformer for Image Restoration (2024)
87 points by teleforce 4 days ago | 8 comments
  • gryfft 2 days ago |
    [2024]
  • TimorousBestie 2 days ago |
    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.

    • FuckButtons 2 days ago |
      I do wonder if a wavelet transform might be better.
      • TimorousBestie 2 days ago |
        I think one can do better with a wavelet, shearlet, or curvelet transform that is adapted to the problem domain at hand. But the uncertainty principle still haunts those transforms, and anyway the goal is to be domain-agile.
  • sorenjan 2 days ago |
    See also: CosAE: Learnable Fourier Series for Image Restoration (2024)

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

  • waynecochran 2 days ago |
    Was there a conclusion?
  • jongala 2 days ago |
    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/).

    • krackers 2 days ago |
      I'd like to see a sequel where the fractional fourier transform is used for image restoration