Quaternion wavelets for image analysis and processing

Using the concepts of two-dimensional Hubert transform and analytic signal, we construct a new quaternion wavelet transform (QWT). The QWT forms a tight frame and can be efficiently computed using a-2-D dual-tree filter bank. The QWT and the 2-D complex wavelet transform (CWT) are related by a unita...

Full description

Saved in:
Bibliographic Details
Main Authors: Wai Lam Chan, Hyeokho Choi, Baraniuk, R.
Format: Conference Proceeding
Language:English
Subjects:
Applied sciences
Artificial intelligence
Computer science
control theory
systems
Continuous wavelet transforms
Exact sciences and technology
Filter bank
Fourier transforms
Image analysis
Image edge detection
Pattern recognition. Digital image processing. Computational geometry
Phase estimation
Quaternions
Signal analysis
Wavelet analysis
Wavelet transforms
Citations: Items that cite this one
Online Access:Request full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Using the concepts of two-dimensional Hubert transform and analytic signal, we construct a new quaternion wavelet transform (QWT). The QWT forms a tight frame and can be efficiently computed using a-2-D dual-tree filter bank. The QWT and the 2-D complex wavelet transform (CWT) are related by a unitary transformation, but the former inherits the quaternion Fourier-transform (QFT) phase properties, which are desirable for image analysis. The quaternion magnitude-phase representation of the QWT directly leads to near shift-invariance and the ability to encode phase shifts in an absolute x-y-coordinate system, which we can use for applications such as edge estimation and statistical image modeling.
ISSN:1522-4880
2381-8549
DOI:10.1109/ICIP.2004.1421758