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

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

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 the two-sphere and other conic sections

Pierre Vandergheynst

We review the construction of the continuous wavelet transform (CWT) on the two-sphere by two methods, the group-theoretical approach and the geometrical method based on conformal invariance. Then we discuss the discretization of the spherical CWT, obtaini ...

2007

Generalized Daubechies Wavelet Families

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We present a generalization of the orthonormal Daubechies wavelets and of their related biorthogonal flavors (Cohen-Daubechies-Feauveau, 9⁄7). Our fundamental constraint is that the scaling functions should reproduce a predefined set of exponential polynom ...

IEEE2007

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

Michaël Unser, Cédric René Jean Vonesch

We present an iterative deconvolution algorithm that minimizes a functional with a non-quadratic wavelet-domain regularization term. Our approach is to introduce subband-dependent parameters into the bound optimization framework of Daubechies et al.; it is ...

Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2007

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

Directionlets: Anisotropic Multidirectional representation with separable filtering

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensio ...

2006

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

The Contourlet Transform: An Efficient Directional Multiresolution Image Representation

Martin Vetterli, Minh Do

The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a "true" two-dimensional transform that can c ...

2005

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

Isotropic Polyharmonic B-Splines: Scaling Functions and Wavelets

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

In this paper, we use polyharmonic B-splines to build multidimensional wavelet bases. These functions are nonseparable, multidimensional basis functions that are localized versions of radial basis functions. We show that Rabut's elementary polyharmonic B-s ...

IEEE2005

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

Graph Chatbot

Chat with Graph Search

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

Wavelets on the two-sphere and other conic sections

Generalized Daubechies Wavelet Families

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

Wavelets on non-Euclidean manifolds

Directionlets: Anisotropic Multidirectional representation with separable filtering

An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order

The Contourlet Transform: An Efficient Directional Multiresolution Image Representation

Exponential-Spline Wavelet Bases

Isotropic Polyharmonic B-Splines: Scaling Functions and Wavelets

The Contourlet Transform: An Efficient Directional Multiresolution Image Representation

Wavelets on the two-sphere and other conic sections

Directionlets: Anisotropic Multidirectional representation with separable filtering

Isotropic Polyharmonic B-Splines: Scaling Functions and Wavelets

Wavelets on non-Euclidean manifolds

A fast iterative thresholding algorithm for wavelet-regularized deconvolution - art. no. 67010D

Generalized Daubechies Wavelet Families

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

An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order

Exponential-Spline Wavelet Bases