Publications related to Wavelets on graphs via spectral graph theory

A fast time-domain algorithm for the assessment of tissue blood flow in laser-Doppler flowmetry

Dimitri Nestor Alice Van De Ville, Chandra Sekhar Seelamantula

In this study, we derive a fast, novel time-domain algorithm to compute the nth-order moment of the power spectral density of the photoelectric current as measured in laser-Doppler flowmetry (LDF). It is well established that in the LDF literature these mo ...

Institute of Physics2010

Efficient Approximate Scaling of Spherical Functions in the Fourier Domain With Generalization to Hyperspheres

Ivan Dokmanic

We propose a simple model for approximate scaling of spherical functions in the Fourier domain. The proposed scaling model is analogous to the scaling property of the classical Euclidean Fourier transform. Spherical scaling is used for example in spherical ...

Institute of Electrical and Electronics Engineers2010

On the power of combinatorial and spectral invariants

We extend the traditional spectral invariants (spectrum and angles) by a stronger polynomial time computable graph invariant based on the angles between projections of standard basis vectors into the eigenspaces (in addition to the usual angles between sta ...

2010

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

A Fast Thresholded Landweber Algorithm for General Wavelet Bases: Application to 3D Deconvolution Microscopy

Michaël Unser, Cédric René Jean Vonesch

Wavelet-domain

ℓ _{ 1 }

-regularization is a promising approach to deconvolution. The corresponding variational problem can be solved using a “thresholded Landweber” (TL) algorithm. While this iterative procedure is simple to implement, it is known to ...

IEEE2008

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

Complex B-Splines

Michaël Unser, Thierry Blu

We propose a complex generalization of Schoenberg's cardinal splines. To this end, we go back to the Fourier domain definition of the B-splines and extend it to complex-valued degrees. We show that the resulting complex B-splines are piecewise modulated po ...

Elsevier2006

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

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

Guest Editorial: Wavelets in Medical Imaging

Michaël Unser

I. Introduction Wavelets are the result of collective efforts that recognized common threads between ideas and concepts that had been independently developed and investigated by distinct research communities. They provide a unifying framework for decompos ...

2003

Wavelets on graphs via spectral graph theory

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A fast time-domain algorithm for the assessment of tissue blood flow in laser-Doppler flowmetry

Efficient Approximate Scaling of Spherical Functions in the Fourier Domain With Generalization to Hyperspheres

On the power of combinatorial and spectral invariants

Wavelets on Graphs via Spectral Graph Theory

A Fast Thresholded Landweber Algorithm for General Wavelet Bases: Application to 3D Deconvolution Microscopy

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

Complex B-Splines

An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order

Isotropic Polyharmonic B-Splines: Scaling Functions and Wavelets

Guest Editorial: Wavelets in Medical Imaging

A fast time-domain algorithm for the assessment of tissue blood flow in laser-Doppler flowmetry

On the power of combinatorial and spectral invariants

Efficient Approximate Scaling of Spherical Functions in the Fourier Domain With Generalization to Hyperspheres

Complex B-Splines

An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order

Wavelets on Graphs via Spectral Graph Theory

Isotropic Polyharmonic B-Splines: Scaling Functions and Wavelets

A Fast Thresholded Landweber Algorithm for General Wavelet Bases: Application to 3D Deconvolution Microscopy

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

Guest Editorial: Wavelets in Medical Imaging