Wavelet statistical models and Besov spaces

We discover a new relationship between two seemingly different image modeling methodologies; the Besov space theory and the wavelet-domain statistical image models. Besov spaces characterize the set of real-world images through a deterministic characterization of the image smoothness, while statistical image models capture the probabilistic properties of images. By establishing a relationship between the Besov norm and the normalized likelihood function under an independent wavelet domain generalized Gaussian model, we obtain a new interpretation of the Besov norm which provides a natural generalization of the theory for practical image processing. Based on this new interpretation of the Besov space, we propose a new image denoising algorithm based on projections onto the convex sets defined in the Besov space: After pointing out the limitations of Besov spaces, we propose possible generalizations using more accurate image models.