Some Remarks on Multiscale Transformations, Stability and Biorthogonality (1991)
| Venue: | Wavelets, Images, and Surface Fitting |
| Citations: | 25 - 13 self |
BibTeX
@INPROCEEDINGS{Dahmen91someremarks,
author = {Wolfgang Dahmen},
title = {Some Remarks on Multiscale Transformations, Stability and Biorthogonality},
booktitle = {Wavelets, Images, and Surface Fitting},
year = {1991},
pages = {157--188},
publisher = {Academic Press}
}
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Abstract
. This paper is concerned with the concepts of stability and biorthogonality for a general framework of multiscale transformations. In particular, stability criteria are derived which do not make use of Fourier transform techniques but rather hinge upon classical Bernstein and Jackson estimates. Therefore they might be useful when dealing with possibly nonuniform discretizations or with bounded domains. x1. Introduction Let c be some string of data c k ; k 2 I, where I is some (finite or possibly infinite) index set. These data could represent grey scale values of a digital image, statistical noisy data, or control points in some curve or surface representation, or approximate solutions of some discretized operator equation. The common ground for these rather different interpretations is that these data could be viewed as coefficients of some expansion f = X k2I c k ' k ; (1:1) where the ' k are (typically scalar-valued shape) functions defined on some domain (or manifold)\Omega (...
