Publications related to Operator-Like Wavelet Bases of L-2(R-d)

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

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

Spectral Properties and Stability of Self-Similar Wave Maps

Roland Donninger

In this thesis the Cauchy problem and in particular the question of singularity formation for co--rotational wave maps from 3+1 Minkowski space to the three--sphere

S^3

is studied. Numerics indicate that self--similar solutions of this model play a cruci ...

University of Vienna2007

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

Directionlets: Anisotropic Multidirectional representation with separable filtering

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensio ...

2006

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

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

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

Which Wavelet Bases Are the Best for Image Denoising?

Michaël Unser, Thierry Blu, Florian Luisier

We use a comprehensive set of non-redundant orthogonal wavelet transforms and apply a denoising method called SUREshrink in each individual wavelet subband to denoise images corrupted by additive Gaussian white noise. We show that, for various images and a ...

SPIE2005

Operator-Like Wavelet Bases of L-2(R-d)

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

Self-Similarity: Part I—Splines and Operators

Inversion de Fourier ponctuelle

Spectral Properties and Stability of Self-Similar Wave Maps

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

Directionlets: Anisotropic Multidirectional representation with separable filtering

Generalized L-Spline Wavelet Bases

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order

Which Wavelet Bases Are the Best for Image Denoising?

Which Wavelet Bases Are the Best for Image Denoising?

Directionlets: Anisotropic Multidirectional representation with separable filtering

Inversion de Fourier ponctuelle

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

Spectral Properties and Stability of Self-Similar Wave Maps

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

Generalized L-Spline Wavelet Bases

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Self-Similarity: Part I—Splines and Operators

An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order