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 - <p style="text-align: justify;">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. &nbsp;</p>