Multifractal wavelet filter of natural images

Natural images are characterized by the multiscaling properties of their co ntrast gradient, in addition to their power spectrum. In this Letter we sho w that those properties uniquely define an intrinsic wavelet and present a suitable technique to obtain it from an ensemble of images. Once this wavel et is known, images can be represented as expansions in the associated wave let basis. The resulting code has the remarkable properties that it separat es independent features at different resolution level, reducing the redunda ncy, and remains essentially unchanged under changes in the power spectrum. The possible generalization of this representation to other systems is dis cussed.