The Monogenic Wavelet Transform

被引：52

作者：

Olhede, Sofia C. ^{[1
]}

Metikas, Georgios ^{[2
]}

机构：

[1] UCL, Dept Stat Sci, London WC1E 6BT, England

[2] Deutsch Bank, London EC2N 2DB, England

来源：

IEEE TRANSACTIONS ON SIGNAL PROCESSING | 2009年 / 57卷 / 09期

基金：

英国工程与自然科学研究理事会;

关键词：

Analytic signal; analytic wavelet transform; Hilbert transform; monogenic signal; Riesz transform; MULTIPLE MORSE WAVELETS; IMAGE-ANALYSIS; SIGNALS;

D O I：

10.1109/TSP.2009.2023397

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

This paper extends the 1-D analytic wavelet transform to the 2-D monogenic wavelet transform. The transformation requires care in its specification to ensure suitable transform coefficients are calculated, and it is constructed so that the wavelet transform may be considered as both local and monogenic. This is consistent with defining the transform as a real wavelet transform of a monogenic signal in analogy with the analytic wavelet transform. Classes of monogenic wavelets are proposed with suitable local properties. It is shown that the monogenic wavelet annihilates anti-monogenic signals, that the monogenic wavelet transform is phase-shift covariant and that the transform magnitude is phase-shift invariant. A simple form for the magnitude and orientation of the isotropic transform coefficients of a unidirectional signal when observed in a rotated frame of reference is derived. The monogenic wavelet ridges of local plane waves are given.

引用

页码：3426 / 3441

页数：16

共 57 条

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[2]

[Anonymous], 1995, TRANSLATION INVARIAN

[3]

Antoine J.P., 2004, Two-Dimensional Wavelets and their Relatives

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