Publications associées à Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

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

Shift-Invariant Spaces from Rotation-Covariant Functions

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

We consider shift-invariant multiresolution spaces generated by rotation-covariant functions ρ in

\mathbb{R}^{ 2 }

. To construct corresponding scaling and wavelet functions, ρ has to be localized with an appropriate multiplier, such that the localized ...

Elsevier2008

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

WSPM: Wavelet-Based Statistical Parametric Mapping

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

Recently, we have introduced an integrated framework that combines wavelet-based processing with statistical testing in the spatial domain. In this paper, we propose two important enhancements of the framework. First, we revisit the underlying paradigm; i. ...

Elsevier2007

Continuous Wavelet Transform on the Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

In this paper we build a Continuous Wavelet Transform (CWT) on the upper sheet of the 2-hyperboloid

H_+^2

. First, we define a class of suitable dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to $SO ...

2007

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

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

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

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

The approximate behavior of wavelets as differential operators is often considered as one of their most fundamental properties. In this paper, we investigate how we can further improve on the wavelet's behavior as differentiator. In particular, we propose ...

SPIE2005

Generalized L-Spline Wavelet Bases

Michaël Unser, Thierry Blu, Ildar Khalidov

We build wavelet-like functions based on a parametrized family of pseudo-differential operators

L _{ v }

that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green func ...

SPIE2005

Similarity solutions for solute transport in fractal porous media using a time-and scale-dependent dispersivity

David Andrew Barry, Fang Liu

A specific form of the Fokker–Planck equation with a time- and scale-dependent dispersivity is presented for modelling solute transport in saturated heterogeneous porous media. By taking a dispersivity in the form of separable power-law dependence on both ...

2005

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

Graph Chatbot

Chattez avec Graph Search

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

Shift-Invariant Spaces from Rotation-Covariant Functions

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

WSPM: Wavelet-Based Statistical Parametric Mapping

Continuous Wavelet Transform on the Hyperboloid

Low-Rate Reduced Complexity Image Compression using Directionlets

Wavelets on non-Euclidean manifolds

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Generalized L-Spline Wavelet Bases

Similarity solutions for solute transport in fractal porous media using a time-and scale-dependent dispersivity

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

Continuous Wavelet Transform on the Hyperboloid

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

Wavelets on non-Euclidean manifolds

Generalized L-Spline Wavelet Bases

Similarity solutions for solute transport in fractal porous media using a time-and scale-dependent dispersivity

Shift-Invariant Spaces from Rotation-Covariant Functions

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

WSPM: Wavelet-Based Statistical Parametric Mapping

Low-Rate Reduced Complexity Image Compression using Directionlets