Author :
Do, Minh N. ; Vetterli, Martin
Author_Institution :
Dept. of Commun. Syst., Swiss Fed. Inst. of Technol., Lausanne, Switzerland
Abstract :
Burt and Adelson (1983) 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.
Keywords :
Laplace transforms; channel bank filters; filtering theory; image reconstruction; image representation; image resolution; image sampling; Laplacian pyramid; continuous-domain frames; dual frame operator; forward transform; frame theory; framing pyramids; multiresolution image representation; noise; optimal linear reconstruction; orthogonal filters; oversampled filterbank; perfect reconstruction; suboptimal image reconstruction; tight frame; Filter bank; Filtering; Frequency; Image coding; Image reconstruction; Laboratories; Laplace equations; Signal processing; Signal resolution; Signal synthesis;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2003.815389
