Function Spaces Based on Wavelet Expansions
Several extensions of Besov spaces are studied. They take into account the distributions of wavelet coefficients at each scale and the correlations between the positions of the large wavelet coefficients. These new spaces allow us to formalize two new notions: the “contour-type” functions, which display the strongest possible correlations, and the “shuffled-type” functions, which display the weakest possible correlations. These notions depend neither on the particular wavelet basis chosen nor on an a priori statistical model. Several examples taken from image and signal processing illustrate these notions.
KeywordsFunction Space Wavelet Coefficient Besov Space Wavelet Basis Dyadic Cube
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