Publications related to Operator-Like Wavelet Bases of $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Universal Bounds And Semiclassical Estimates For Eigenvalues Of Abstract Schrodinger Operators

We prove trace inequalities for a self-adjoint operator on an abstract Hilbert space, which extend those known previously for Laplacians and Schrodinger operators, freeing them from restrictive assumptions on the nature of the spectrum and allowing operato ...

2010

Fractional Brownian Vector Fields

Michaël Unser, Pouya Dehghani Tafti

This work puts forward an extended definition of vector fractional Brownian motion (fBm) using a distribution theoretic formulation in the spirit of Gel′fand and Vilenkin's stochastic analysis. We introduce random vector fields that share the statistical i ...

SIAM2010

Operator-like wavelets with application to functional magnetic resonance imaging

Ildar Khalidov

We introduce a new class of wavelets that behave like a given differential operator L. Our construction is inspired by the derivative-like behavior of classical wavelets. Within our framework, the wavelet coefficients of a signal y are the samples of a smo ...

EPFL2009

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Michaël Unser, Kunal Narayan Chaudhury

We propose an amplitude-phase representation of the dual-tree complex wavelet transform (DT-ℂWT) which provides an intuitive interpretation of the associated complex wavelet coefficients. The representation, in particular, is based on the shifting action o ...

SPIE2009

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

Michaël Unser, Dimitri Nestor Alice Van De Ville, Pouya Dehghani Tafti

In this contribution, we study the notion of affine invariance (specifically, invariance to the shifting, scaling, and rotation of the coordinate system) as a starting point for the development of mathematical tools and approaches useful in the characteriz ...

IEEE2009

An iterative domain decomposition algorithm for the grad(div) operator

Michel Deville, Etienne Ahusborde

This paper describes an iterative solution technique for partial differential equations involving the grad(div) operator, based on a domain decomposition. Iterations are performed to solve the solution on the interface. We identify the transmission relatio ...

2009

Wavelets on Graphs via Spectral Graph Theory

Pierre Vandergheynst, Rémi Gribonval

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite graph. We define a notion of scaling using the graph analogue of the Fourier domain, namely the space of eigenfunctions forming the sp ...

2008

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

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

Operator-Like Wavelet Bases of $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

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Universal Bounds And Semiclassical Estimates For Eigenvalues Of Abstract Schrodinger Operators

Fractional Brownian Vector Fields

Operator-like wavelets with application to functional magnetic resonance imaging

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

An iterative domain decomposition algorithm for the grad(div) operator

Wavelets on Graphs via Spectral Graph Theory

Shift-Invariant Spaces from Rotation-Covariant Functions

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

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

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

Fractional Brownian Vector Fields

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

An iterative domain decomposition algorithm for the grad(div) operator

Universal Bounds And Semiclassical Estimates For Eigenvalues Of Abstract Schrodinger Operators

Operator-like wavelets with application to functional magnetic resonance imaging

Wavelets on Graphs via Spectral Graph Theory

Shift-Invariant Spaces from Rotation-Covariant Functions

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