Non-separable bidimensional wavelet bases.

Cohen, Albert, and Daubechies, Ingrid. "Non-separable bidimensional wavelet bases.." Revista Matemática Iberoamericana 9.1 (1993): 51-137. <http://eudml.org/doc/39836>.

@article{Cohen1993,
abstract = {We build orthonormal and biorthogonal wavelet bases of L2(R2) with dilation matrices of determinant 2. As for the one dimensional case, our construction uses a scaling function which solves a two-scale difference equation associated to a FIR filter. Our wavelets are generated from a single compactly supported mother function. However, the regularity of these functions cannot be derived by the same approach as in the one dimensional case. We review existing techniques to evaluate the regularity of wavelets, and we introduce new methods which allow to estimate the smoothness of non-separable wavelets and scaling functions in the most general situations. We illustrate these with several examples.},
author = {Cohen, Albert, Daubechies, Ingrid},
journal = {Revista Matemática Iberoamericana},
keywords = {Ondículas; Bases ortonormales; Matrices de dilatación; Funciones de escala; Filtros digitales; two-dimensional wavelet bases; univariate wavelet series representations; scaling function; two-scale difference equation; FIR filter; smoothness},
language = {eng},
number = {1},
pages = {51-137},
title = {Non-separable bidimensional wavelet bases.},
url = {http://eudml.org/doc/39836},
volume = {9},
year = {1993},
}

TY - JOUR
AU - Cohen, Albert
AU - Daubechies, Ingrid
TI - Non-separable bidimensional wavelet bases.
JO - Revista Matemática Iberoamericana
PY - 1993
VL - 9
IS - 1
SP - 51
EP - 137
AB - We build orthonormal and biorthogonal wavelet bases of L2(R2) with dilation matrices of determinant 2. As for the one dimensional case, our construction uses a scaling function which solves a two-scale difference equation associated to a FIR filter. Our wavelets are generated from a single compactly supported mother function. However, the regularity of these functions cannot be derived by the same approach as in the one dimensional case. We review existing techniques to evaluate the regularity of wavelets, and we introduce new methods which allow to estimate the smoothness of non-separable wavelets and scaling functions in the most general situations. We illustrate these with several examples.
LA - eng
KW - Ondículas; Bases ortonormales; Matrices de dilatación; Funciones de escala; Filtros digitales; two-dimensional wavelet bases; univariate wavelet series representations; scaling function; two-scale difference equation; FIR filter; smoothness
UR - http://eudml.org/doc/39836
ER -