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Discretization-invariant Image Processing based on Fourier Neural Operators

SpectralConv2d

  • in_channels, out_channels: clear
  • paramterization: 'spatial', 'spectral' how to parameterize the kernel. Convertable, but differences in training opt
  • in_shape: only applies for param='spatial'. Options:
    • in_shape=None: spatial kernel doman varies with input resolution in the same way as normal CNNS
    • in_shape=[N,M]: kernel to image relation is apadpted to kernel shape to in_shape relation.
  • out_shape: applies for both parametrizations Determines output shape after convolution but before striding.
    • out_shape=None: this yields out_shape equal to the shape of the input
    • out_shape=[N,M]: resizng via trigonometric interpolation. Here, N,M can not depend on the input shape.
  • stride: usual striding, like for CNNs.
  • odd: only applies for param='spectral'. Determines if the parametrized kernel fft $\mathcal{F}(k)$ has odd or even width.
  • norm: determines the norm to be used in FFT. If out_shape is not None the norm is recommended to be choosen as norm='forward'.

A normal CNN can be mimicked by using in_shape=None, out_shape = None

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