Deep convolutional neural networks on cartoon functions

@article{Grohs2016DeepCN,
  title={Deep convolutional neural networks on cartoon functions},
  author={Philipp Grohs and Thomas Wiatowski and Helmut B{\"o}lcskei},
  journal={2016 IEEE International Symposium on Information Theory (ISIT)},
  year={2016},
  pages={1163-1167}
}
Wiatowski and Bölcskei, 2015, proved that deformation stability and vertical translation invariance of deep convolutional neural network-based feature extractors are guaranteed by the network structure per se rather than the specific convolution kernels and non-linearities. While the translation invariance result applies to square-integrable functions, the deformation stability bound holds for band-limited functions only. Many signals of practical relevance (such as natural images) exhibit… CONTINUE READING
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