The abstract reads:
This paper presents a statistical model for textures that uses a non-negative decomposition on a set of local atoms learned from an exemplar. This model is described by the variances and kurtosis of the marginals of the decomposition of patches in the learned dictionary. A fast sampling algorithm allows to draw a typical image from this model. The resulting texture synthesis captures the geometric features of the original exemplar. To speed up synthesis and generate structures of various sizes, a multi-scale process is used. Applications to texture synthesis, image inpainting and texture segmentation are presented.
Please note his comment that the sparsity requirement does not help much:
An explicit sparsity prior can be added into this process  to enforce the constraints $||xj ||_0 < \tau$ required by equation (1). In practice, this did not result in a noticeable enhancement for texture modeling.This is surprising (see Sparsity or positivity ?) but one might not be so lucky for other types of signals. Let us not forget that while curvelets or contourlets seem doing a good job at describing contours and therefore enable a better Compressive Sampling, they do not address textures (which is the reason of this paper), nor time related or hyperspectral compressible bases.