Wavelet statistical models and Besov spaces

Hyeokho Choi; Richard G. Baraniuk

doi:10.1117/12.366806

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26 October 1999 Wavelet statistical models and Besov spaces

Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366806
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

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. Base don 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 space, we propose possible generalizations using more accurate image models.

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Hyeokho Choi and Richard G. Baraniuk "Wavelet statistical models and Besov spaces", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366806

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