# Non-separable bidimensional wavelet bases.

Albert Cohen; Ingrid Daubechies

Revista Matemática Iberoamericana (1993)

- Volume: 9, Issue: 1, page 51-137
- ISSN: 0213-2230

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topCohen, 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 -

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