Wavelet Statistical Models and Besov Spaces

We discover a new relationship between two seemingly diierent 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 deened in the Besov space. After pointing out the limitations of Besov spaces, we propose possible generalizations using more accurate image models.