  Deep learning based methods for single-image super-resolution (SR) have drawn
a lot of attention lately. In particular, various papers have shown that the
learning stage can be performed on a single image, resulting in the so-called
internal approaches. The SinGAN method is one of these contributions, where the
distribution of image patches is learnt on the image at hand and propagated at
finer scales. Now, there are situations where some statistical a priori can be
assumed for the final image. In particular, many natural phenomena yield images
having power law Fourier spectrum, such as clouds and other texture images. In
this work, we show how such a priori information can be integrated into an
internal super-resolution approach, by constraining the learned up-sampling
procedure of SinGAN. We consider various types of constraints, related to the
Fourier power spectrum, the color histograms and the consistency of the
upsampling scheme. We demonstrate on various experiments that these constraints
are indeed satisfied, but also that some perceptual quality measures can be
improved by the proposed approach.
