We provide a new model for texture synthesis based on a multiscale, multilayer feature extractor. Within the model, textures are represented by a set of statistics computed from ReLU wavelet coefficients at different layers, scales and orientations. A new image is synthesized by matching the target statistics via an iterative projection algorithm. We explain the necessity of the different types of pre-defined wavelet filters used in our model and the advantages of multilayer structures for image synthesis. We demonstrate the power of our model by generating samples of high quality textures and providing insights into deep representations for texture images.