Information-theoretic interpretation of Besov spaces

Hyeokho Choi; Richard G. Baraniuk

doi:10.1117/12.408657

4 December 2000 Information-theoretic interpretation of Besov spaces

Hyeokho Choi, Richard G. Baraniuk

Proceedings Volume 4119, Wavelet Applications in Signal and Image Processing VIII; (2000) https://doi.org/10.1117/12.408657
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

Besov spaces classify signals and images through the Besov norm, which is based on a deterministic smoothness measurement. Recently, we revealed the relationship between the Besov norm and the likelihood of an independent generalized Gaussian wavelet probabilistic model. In this paper, we extend this result by providing an information- theoretical interpretation of the Besov norm as the Shannon codelength for signal compression under this probabilistic mode. This perspective unites several seemingly disparate signal/image processing methods, including denoising by Besov norm regularization, complexity regularized denoising, minimum description length processing, and maximum smoothness interpolation. By extending the wavelet probabilistic model, we broaden the notion of smoothness space to more closely characterize real-world data. The locally Gaussian model leads directly to a powerful wavelet- domain. Wiener filtering algorithm for denoising.

Citation Download Citation

Hyeokho Choi and Richard G. Baraniuk "Information-theoretic interpretation of Besov spaces", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); https://doi.org/10.1117/12.408657

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