Publications related to The Fractional Hilbert Transform And Dual-Tree Gabor-Like Wavelet Analysis

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Daniel Sage

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-value ...

Institute of Electrical and Electronics Engineers2009

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Michaël Unser, Kunal Narayan Chaudhury

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions-the B-spline factorization theorem. In particular, starting from well-localized sc ...

IEEE2009

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

Michaël Unser, Dimitri Nestor Alice Van De Ville

Based on the class of complex gradient-Laplace operators, we show the design of a non-separable two-dimensional wavelet basis from a single and analytically defined generator wavelet function. The wavelet decomposition is implemented by an efficient FFT-ba ...

SPIE2009

The Monogenic Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Katarina Balac

We introduce a family of real and complex wavelet bases of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) that are directly linked to the Laplace and Riesz operators. The crucial point is that the family is closed with respect to the Riesz transform which maps a re ...

EURASIP2008

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Michaël Unser, Dimitri Nestor Alice Van De Ville

A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer ad ...

Institute of Electrical and Electronics Engineers2008

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Dimitri Nestor Alice Van De Ville

We present multiresolution spaces of complex rotation-covariant functions, deployed on the 2-D hexagonal lattice. The designed wavelets, which are complex-valued, provide an important phase information for image analysis, which is missing in the discrete w ...

SPIE2007

Wavelets on non-Euclidean manifolds

Iva Bogdanova Vandergheynst

This dissertation investigates wavelets as a multiscale tool on non-Euclidean manifolds. The growing importance of using non-Euclidean manifolds as a geometric model for data comes from the diversity of the data collected. In this work we mostly deal with ...

EPFL2006

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Pierre Vandergheynst, Oscar Divorra Escoda

In this work, we study the effect of inserting spatially local temporal adaptivity to motion compensated frame adaptive transforms for video coding. Motion compensation aligns the temporal wavelet decomposition along motion trajectories. However, valid tra ...

2004

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Michaël Unser, Dimitri Nestor Alice Van De Ville, Daniel Sage

Microscopy imaging often suffers from limited depth-of-focus. However, the specimen can be “optically sectioned” by moving the object along the optical axis; different areas appear in focus in different images. Extended depth-of-focus is a fusion algorithm ...

IEEE2004

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

Michaël Unser, Dimitri Nestor Alice Van De Ville, Daniel Sage

Microscopy imaging often suffers from limited depth-of-field. However, the specimen can be “optically sectioned” by moving the object along the optical axis. Then different areas appear in focus in different images. Extended depth-of-field is a fusion algo ...

Wiley-Liss2004

The Fractional Hilbert Transform And Dual-Tree Gabor-Like Wavelet Analysis

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Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

The Monogenic Riesz-Laplace Wavelet Transform

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Wavelets on non-Euclidean manifolds

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Wavelets on non-Euclidean manifolds

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

The Monogenic Riesz-Laplace Wavelet Transform

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images