Hypercomplex spectral transformations
Hypercomplex spectral transformations
Local frequency analysis with two-dimensional wavelet transform
Signal Processing
Time-frequency analysis: theory and applications
Time-frequency analysis: theory and applications
Non-commutative hypercomplex Fourier tranforms of multidimensional signals
Geometric computing with Clifford algebras
Motion Smoothing Using Wavelets
Journal of Intelligent and Robotic Systems
Quaternion Gabor Filters for Local Structure Classification
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 1 - Volume 1
Quaternion Wavelets for Moving Volume Representation
IV '01 Proceedings of the Fifth International Conference on Information Visualisation
The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space
Journal of Mathematical Imaging and Vision
International Journal of Computer Vision
Higher-order properties of analytic wavelets
IEEE Transactions on Signal Processing
Wigner distributions and ambiguity functions of 2-D quaternionic and monogenic signals
IEEE Transactions on Signal Processing - Part II
IEEE Transactions on Signal Processing
The homomorphic analytic signal
IEEE Transactions on Signal Processing
The phaselet transform-an integral redundancy nearly shift-invariant wavelet transform
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Cramer-Rao bounds for wavelet transform-based instantaneous frequency estimates
IEEE Transactions on Signal Processing
Multiple Multidimensional Morse Wavelets
IEEE Transactions on Signal Processing
Localisation of Geometric Anisotropy
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Hypercomplex signals-a novel extension of the analytic signal tothe multidimensional case
IEEE Transactions on Signal Processing
Analysis of singularities from modulus maxima of complex wavelets
IEEE Transactions on Information Theory
Nonlinear image operators for the evaluation of local intrinsic dimensionality
IEEE Transactions on Image Processing
Long-correlation image models for textures with circular and elliptical correlation structures
IEEE Transactions on Image Processing
Multidimensional, mapping-based complex wavelet transforms
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Image Modeling Using Interscale Phase Properties of Complex Wavelet Coefficients
IEEE Transactions on Image Processing
Image Denoising Using Derotated Complex Wavelet Coefficients
IEEE Transactions on Image Processing
Directional Multiscale Amplitude and Phase Decomposition by the Monogenic Curvelet Transform
SIAM Journal on Imaging Sciences
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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.