Framing Pyramids (2003)
| Venue: | IEEE TRANSACTIONS ON SIGNAL PROCESSING |
| Citations: | 38 - 6 self |
BibTeX
@ARTICLE{Do03framingpyramids,
author = {Minh N. Do and Martin Vetterli},
title = {Framing Pyramids},
journal = {IEEE TRANSACTIONS ON SIGNAL PROCESSING},
year = {2003},
volume = {51},
pages = {2329--2342}
}
Years of Citing Articles
OpenURL
Abstract
In 1983, Burt and Adelson introduced the Laplacian pyramid (LP) as a multiresolution representation for images. We study the LP using the frame theory, and this reveals that the usual reconstruction is suboptimal. We show that the LP with orthogonal filters is a tight frame, and thus, the optimal linear reconstruction using the dual frame operator has a simple structure that is symmetric with the forward transform. In more general cases, we propose an efficient filterbank (FB) for the reconstruction of the LP using projection that leads to a proved improvement over the usual method in the presence of noise. Setting up the LP as an oversampled FB, we offer a complete parameterization of all synthesis FBs that provide perfect reconstruction for the LP. Finally, we consider the situation where the LP scheme is iterated and derive the continuous -domain frames associated with the LP.







