Anisotropic Wavelet Bases and Restricted Nonlinear Approximation

Restricted Nonlinear Approximation 1

Restricted Nonlinear Approximation

We introduce a new form of nonlinear approximation called restricted approximation. It is a generalization of n-term wavelet approximation in which a weight function is used to control the terms in the wavelet expansion of the approximant. This form of approximation occurs in statistical estimation and in the characterization of interpolation spaces for certain pairs of L p and Besov spaces. We...

Restricted Non-linear Approximation in Sequence Spaces and Applications to Wavelet Bases and Interpolation

Restricted non-linear approximation is a type of N-term approximation where a measure ν on the index set (rather than the counting measure) is used to control the number of terms in the approximation. We show that embeddings for restricted non-linear approximation spaces in terms of weighted Lorentz sequence spaces are equivalent to Jackson and Bernstein type inequalities, and also to the upper...

Anisotropic 3-D wavelet packet bases for video coding

Video coding algorithms based on 3-D wavelet transforms exist which have a competitive rate-distortion performance and are very fast because motion compensation is not needed. The compression efficiency of these algorithms can be increased by the use of more general wavelet packet transforms. Anisotropic wavelet packets are an even more generalized type of wavelet transform, where multidimensio...

Piecewise tensor product wavelet bases by extensions and approximation rates

In this chapter, we present some of the major results that have been achieved in the context of the DFG-SPP project “Adaptive Wavelet Frame Methods for Operator Equations: Sparse Grids, Vector-Valued Spaces and Applications to Nonlinear Inverse Problems”. This project has been concerned with (nonlinear) elliptic and parabolic operator equations on nontrivial domains as well as with related inve...