Directional hypercomplex wavelets for multidimensional signal analysis and processing

Wai Lam Chan, Hyeokho Choi, Richard G. Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

33 Scopus citations

Abstract

We extend the wavelet transform to handle multidimensional signals that are smooth save for singularities along lower-dimensional manifolds. We first generalize the complex wavelet transform to higher dimensions using a multidimensional Hilbert transform. Then, using the resulting hypercomplex wavelet transform (HWT) as a building block, we construct new classes of nearly shift-invariant wavelet frames that are oriented along lower-dimensional subspaces. The HWT can be computed efficiently using a 1-D dual-tree complex wavelet transform along each signal axis. We demonstrate how the HWT can be used for fast line detection in 3-D.

Original languageEnglish (US)
Title of host publicationICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume3
StatePublished - 2004
EventProceedings - IEEE International Conference on Acoustics, Speech, and Signal Processing - Montreal, Que, Canada
Duration: May 17 2004May 21 2004

Other

OtherProceedings - IEEE International Conference on Acoustics, Speech, and Signal Processing
CountryCanada
CityMontreal, Que
Period5/17/045/21/04

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing
  • Acoustics and Ultrasonics

Fingerprint Dive into the research topics of 'Directional hypercomplex wavelets for multidimensional signal analysis and processing'. Together they form a unique fingerprint.

Cite this