Application of non-linear transform coding to image processing

Sparse coding learns its basis non-linearly, but the basis elements are still linearly combined to form an image. Is this linear combination of basis elements a good model for natural images? We here use a non-linear synthesis rule, such that at each location in the image the point-wise maximum over all basis elements is used to synthesize the image. We present algorithms for image approximation and basis learning using this synthesis rule. With these algorithms we explore the the pixel-wise maximum over the basis elements as an alternative image model and thus contribute to the problem of finding a proper representation of natural images.