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.

Date Published: 4 December 2000
PDF: 11 pages
Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); doi: 10.1117/12.408657

Published in SPIE Proceedings Vol. 4119:
Wavelet Applications in Signal and Image Processing VIII
Akram Aldroubi; Andrew F. Laine; Michael A. Unser, Editor(s)