Publications related to Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization

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 Optimal Time-Frequency Localization

Michaël Unser, Kunal Narayan Chaudhury

We propose a novel method of constructing exact Hilbert transform (HT) pairs of wavelet bases using fractional B-splines and state necessary and sufficient conditions for generating such wavelet pairs. In particular, we demonstrate how HT pairs of biorthog ...

IEEE2008

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

Exponential-Spline Wavelet Bases

Michaël Unser, Ildar Khalidov

We build a multiresolution analysis based on shift-invariant exponential B-spline spaces. We construct the basis functions for these spaces and for their orthogonal complements. This yields a new family of wavelet-like basis functions of

L _{ 2 }

, wit ...

IEEE2005

Generalized Daubechies Wavelets

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We present a generalization of the Daubechies wavelet family. The context is that of a non-stationary multiresolution analysis—i.e., a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. ...

IEEE2005

An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order

Michaël Unser, Dimitri Nestor Alice Van De Ville

We present a new family of two-dimensional and three-dimensional orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order λ, which may be nonint ...

IEEE2005

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

Isotropic-Polyharmonic B-Splines and Wavelets

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

We propose the use of polyharmonic B-splines to build non-separable two-dimensional wavelet bases. The central idea is to base our design on the isotropic polyharmonic B-splines, a new type of polyharmonic B-splines that do converge to a Gaussian as the or ...

IEEE2004

A New Family of Complex Rotation-Covariant Multiresolution Bases in 2D

Michaël Unser, Thierry Blu

We present complex rotation-covariant multiresolution families aimed for image analysis. Since they are complex-valued functions, they provide the important phase information, which is missing in the discrete wavelet transform with real wavelets. Our basis ...

SPIE2003

Fractional Wavelets, Derivatives, and Besov Spaces

Michaël Unser, Thierry Blu

We show that a multi-dimensional scaling function of order γ (possibly fractional) can always be represented as the convolution of a polyharmonic B-spline of order γ and a distribution with a bounded Fourier transform which has neither order nor smoothness ...

SPIE2003

Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization

Graph Chatbot

Chat with Graph Search

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Construction of Hilbert Transform Pairs of Wavelet Bases and Optimal Time-Frequency Localization

Wavelets on non-Euclidean manifolds

Exponential-Spline Wavelet Bases

Generalized Daubechies Wavelets

An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Isotropic-Polyharmonic B-Splines and Wavelets

A New Family of Complex Rotation-Covariant Multiresolution Bases in 2D

Fractional Wavelets, Derivatives, and Besov Spaces

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Exponential-Spline Wavelet Bases

Wavelets on non-Euclidean manifolds

Construction of Hilbert Transform Pairs of Wavelet Bases and Optimal Time-Frequency Localization

An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order

Isotropic-Polyharmonic B-Splines and Wavelets

A New Family of Complex Rotation-Covariant Multiresolution Bases in 2D

Fractional Wavelets, Derivatives, and Besov Spaces

Generalized Daubechies Wavelets

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding