Nonlinear wavelet approximation in anisotropic Besov spaces
Abstract
We introduce new anisotropic wavelet decompositions associated with the smoothness β, β = (β1, …, βd), β 1, …, βd > 0 of multi-dimensional data as measured in anisotropic Besov spaces Bβ. We give the rate of compression of these wavelet decompositions of functions f ∈ Bβ. Finally, we prove that, among a general class of anisotropic wavelet decompositions of a function f ∈ Bβ the anisotropic wavelet decomposition associated with β yields the optimal rate of compression of the wavelet decomposition of f.
Degree
Ph.D.
Advisors
Lucier, Purdue University.
Subject Area
Mathematics
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