Publications related to Exponential-Spline Wavelet Bases

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

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 ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

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

The Marr Wavelet Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

We introduce a new semi-orthogonal complex wavelet basis of

L _{ 2 }

(\mathbb{R} ^{ 2 }

). The basis functions are associated to the complex gradient-Laplace operator, which plays a central role in image processing. We define analytically a single- ...

IEEE2008

Construction of wavelet bases that mimic the behaviour of some given operator - art. no. 67010S

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

Probably, the most important property of wavelets for signal processing is their multiscale derivative-like behavior when applied to functions. In order to extend the class of problems that can profit of wavelet-based techniques, we propose to build new fa ...

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

Construction of Wavelet Bases That Mimic the Behaviour of Some Given Operator

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

Probably the most important property of wavelets for signal processing is their multiscale derivative-like behavior when applied to functions. In order to extend the class of problems that can profit of wavelet-based techniques, we propose to build new fam ...

SPIE2007

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

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

Low-Rate Reduced Complexity Image Compression using Directionlets

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

The standard separable two-dimensional (2-D) wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to capture efficiently one-dimensional (1-D) disco ...

2006

Superrigidity for irreducible lattices and geometric splitting

Nicolas Monod

We prove general superrigidity results for actions of irreducible lattices on CAT(0) spaces; first, in terms of the ideal boundary, and then for the intrinsic geometry (including for infinite-dimensional spaces). In particular, one obtains a new and self-c ...

2006

Exponential-Spline Wavelet Bases

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

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

The Marr Wavelet Pyramid

Construction of wavelet bases that mimic the behaviour of some given operator - art. no. 67010S

Construction of Wavelet Bases That Mimic the Behaviour of Some Given Operator

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

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

Wavelets on non-Euclidean manifolds

Low-Rate Reduced Complexity Image Compression using Directionlets

Superrigidity for irreducible lattices and geometric splitting

The Marr Wavelet Pyramid

Wavelets on non-Euclidean manifolds

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

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

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

Construction of wavelet bases that mimic the behaviour of some given operator - art. no. 67010S

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

Low-Rate Reduced Complexity Image Compression using Directionlets

Construction of Wavelet Bases That Mimic the Behaviour of Some Given Operator

Superrigidity for irreducible lattices and geometric splitting