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Wavelet Steerability and the Higher-Order Riesz Transform

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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

Self-Similarity: Part I—Splines and Operators

Michaël Unser, Thierry Blu

The central theme of this pair of papers (Parts I and II in this issue) is self-similarity, which is used as a bridge for connecting splines and fractals. The first part of the investigation is deterministic, and the context is that of L-splines; these are ...

IEEE2007

Inversion de Fourier ponctuelle

Emanuel Enrico Seifert

Let f be an integrable function on RN, a a point in RN and B a complex number. If the mean value of f on the sphere of centre a and radius r tends to B when r tends to 0, we show that the Fourier integral at a of f is summable to B in Cesàro means of order ...

EPFL2007

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

From Differential Equations to the Construction of New Wavelet-Like Bases

Michaël Unser, Ildar Khalidov

In this paper, an approach is introduced based on differential operators to construct wavelet-like basis functions. Given a differential operator L with rational transfer function, elementary building blocks are obtained that are shifted replicates of the ...

IEEE2006

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

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

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

Generalized Daubechies Wavelets

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We present a generalization of the Daubechies wavelet family. The context is that of a non-stationary multiresolution analysis—i.e., a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. ...

IEEE2005

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