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.

翻译：近年来，基于深度学习的单图像超分辨率方法引起了广泛关注。特别地，多项研究表明，学习阶段可在单张图像上完成，由此催生了所谓的"内部方法"。SinGAN方法即是此类贡献之一，该方法在目标图像上学习图像补丁的分布，并逐级向更精细尺度传播。然而，在某些场景下，最终图像可被假定具有特定的统计先验信息。例如，云朵及其他纹理图像等许多自然现象产生的图像，均具有幂律傅里叶谱特性。本研究通过约束SinGAN学习到的上采样过程，展示了如何将此类先验信息整合至内部超分辨率方法中。我们考虑了多种约束类型，涉及傅里叶功率谱、颜色直方图以及上采样方案的一致性。多项实验表明，这些约束不仅能被有效满足，而且所提方法还能提升某些感知质量指标。