The Monogenic Wavelet Transform

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-valued (primary) wavelet basis of L(2) (R(2)) into a complex one. The Riesz operator is also steerable in the sense that it give access to the Hil...

The Monogenic Synchrosqueezed Wavelet Transform: A tool for the Decomposition/Demodulation of AM-FM images

The synchrosqueezing method aims at decomposing 1D functions as superpositions of a small number of “Intrinsic Modes”, supposed to be well separated both in time and frequency. Based on the unidimensional wavelet transform and its reconstruction properties, the synchrosqueezing transform provides a powerful representation of multicomponent signals in the time-frequency plane, together with a re...

Breast abnormalities segmentation using the wavelet transform coefficients aggregation

Introduction: Breast cancer is the most common cancer among women in the world. The automatic detection of masses in digital mammograms is a challenging task and a major step in the development of breast cancer CAD systems. In this study, we introduce a new method for automatic detection of suspicious mass candidate (SMC) regions in a mammogram. Methods: Mammography is widely used for the early...

Steerable wavelet transforms and monogenic image analysis

Linearized Riesz transform and quasi-monogenic shearlets

The only quadrature operator of order two on L2(R) which covaries with orthogonal transforms, in particular rotations is (up to the sign) the Riesz transform. This property was used for the construction of monogenic wavelets and curvelets. Recently, shearlets were applied for various signal processing tasks. Unfortunately, the Riesz transform does not correspond with the shear operation. In thi...