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Volume 22, Issue 6
Hat Average Multiresolution with Error Control in 2-D

Sergio Amat

J. Comp. Math., 22 (2004), pp. 777-790.

Published online: 2004-12

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  • Abstract

Multiresolution representations of data are a powerful tool in data compression. For a proper adaptation to the singularities, it is crucial to develop nonlinear methods which are not based on tensor product. The hat average framework permets develop adapted schemes for all types of singularities. In contrast with the wavelet framework these representations cannot be considered as a change of basis, and the stability theory requires different considerations. In this paper, non separable two-dimensional hat average multiresolution processing algorithms that ensure stability are introduced. Explicit error bounds are presented.  

  • Keywords

Stability, Hat average, Multiresolution, Non separable.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-22-777, author = {Sergio Amat }, title = {Hat Average Multiresolution with Error Control in 2-D}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {6}, pages = {777--790}, abstract = {

Multiresolution representations of data are a powerful tool in data compression. For a proper adaptation to the singularities, it is crucial to develop nonlinear methods which are not based on tensor product. The hat average framework permets develop adapted schemes for all types of singularities. In contrast with the wavelet framework these representations cannot be considered as a change of basis, and the stability theory requires different considerations. In this paper, non separable two-dimensional hat average multiresolution processing algorithms that ensure stability are introduced. Explicit error bounds are presented.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8866.html} }
TY - JOUR T1 - Hat Average Multiresolution with Error Control in 2-D AU - Sergio Amat JO - Journal of Computational Mathematics VL - 6 SP - 777 EP - 790 PY - 2004 DA - 2004/12 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8866.html KW - Stability, Hat average, Multiresolution, Non separable. AB -

Multiresolution representations of data are a powerful tool in data compression. For a proper adaptation to the singularities, it is crucial to develop nonlinear methods which are not based on tensor product. The hat average framework permets develop adapted schemes for all types of singularities. In contrast with the wavelet framework these representations cannot be considered as a change of basis, and the stability theory requires different considerations. In this paper, non separable two-dimensional hat average multiresolution processing algorithms that ensure stability are introduced. Explicit error bounds are presented.  

Sergio Amat . (2004). Hat Average Multiresolution with Error Control in 2-D. Journal of Computational Mathematics. 22 (6). 777-790. doi:
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