Published in Natural Scene Statistics Meeting, Sep 1997.
I present a simple statistical model for images in the wavelet transform domain. The model characterizes the joint densities of coefficients at adjacent spatial locations, adjacent orientations, and adjacent spatial scales. The model accounts for the statistics of a wide variety of images. The model also suggests a nonlinear form of optimal representation, which I call ``normalized component analysis'', in which each wavelet coefficient is divided by a linear combination of coefficient magnitudes corresponding to basis functions at adjacent locations, orientations and scales. These statistical results provide theoretical motivation for the normalization models that have recently become popular in modeling the behavior of striate cortical neurons. In addition, I'll demonstrate the power of the decomposition for applications such as image compression, enhancement and synthesis.