Framing pyramids

Minh N. Do, Martin Vetterli

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)2329-2342
Number of pages14
JournalIEEE Transactions on Signal Processing
Volume51
Issue number9
DOIs
StatePublished - Sep 2003
Externally publishedYes

Keywords

  • Filterbanks
  • Framelets
  • Frames
  • Laplacian pyramid
  • Multiresolution signal processing
  • Projection
  • Pseudo inverse
  • Wavelets

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

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