  State-of-the-art maximum entropy models for texture synthesis are built from
statistics relying on image representations defined by convolutional neural
networks (CNN). Such representations capture rich structures in texture images,
outperforming wavelet-based representations in this regard. However, conversely
to neural networks, wavelets offer meaningful representations, as they are
known to detect structures at multiple scales (e.g. edges) in images. In this
work, we propose a family of statistics built upon non-linear wavelet based
representations, that can be viewed as a particular instance of a one-layer
CNN, using a generalized rectifier non-linearity. These statistics
significantly improve the visual quality of previous classical wavelet-based
models, and allow one to produce syntheses of similar quality to
state-of-the-art models, on both gray-scale and color textures.
