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Comparison of Wavelets from the Point of View of Their Approximation Error

Publications associées (71)

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Discrete Wavelet Frames on the Sphere

Pierre Vandergheynst, Laurent Jacques, Iva Bogdanova Vandergheynst

In this paper the Continuous Wavelet Transform on the sphere is exploited to build the asociated Discrete Wavelet Frames. First, the half-continuous frames, i.e. frames where the position remains a continuous variable, is presented and then the fully discr ...

EUSIPCO2004

Fractional Splines, Wavelet Bases, and Applications

Michaël Unser

The purpose of this presentation is to describe a recent family of basis functions—the fractional B-splines—which appear to be intimately connected to fractional calculus. Among other properties, we show that they are the convolution kernels that link the ...

ENSEIRB2004

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 Versus Resels in the Context of fMRI: Establishing the Link with SPM

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

Statistical Parametric Mapping (SPM) is a widely deployed tool for detecting and analyzing brain activity from fMRI data. One of SPM's main features is smoothing the data by a Gaussian filter to increase the SNR. The subsequent statistical inference is bas ...

SPIE2003

Fractional Wavelets, Derivatives, and Besov Spaces

Michaël Unser, Thierry Blu

We show that a multi-dimensional scaling function of order γ (possibly fractional) can always be represented as the convolution of a polyharmonic B-spline of order γ and a distribution with a bounded Fourier transform which has neither order nor smoothness ...

SPIE2003

Splines and Wavelets: New Perspectives for Pattern Recognition

Michaël Unser

We provide an overview of spline and wavelet techniques with an emphasis on applications in pattern recognition. The presentation is divided in three parts. In the first one, we argue that the spline representation is ideally suited for all processing task ...

DAGM e. V2003

Mathematical Properties of the JPEG2000 Wavelet Filters

Michaël Unser, Thierry Blu

The LeGall 5⁄3 and Daubechies 9⁄7 filters have risen to special prominence because they were selected for inclusion in the JPEG2000 standard. Here, we determine their key mathematical features: Riesz bounds, order of approximation, and regularity (Hölder a ...

IEEE2003

Wavelet Footprints: Theory, Algorithms and Applications

Martin Vetterli, Pier Luigi Dragotti

In recent years, wavelet-based algorithms have been successful in different signal processing tasks. The wavelet trans- form is a powerful tool because it manages to represent both tran- sient and stationary behaviors of a signal with few transform coeffi- ...

2003

An Error Analysis for the Sampling of Periodic Signals

Michaël Unser, Thierry Blu, Mathews Jacob

We analyze the representation of periodic signals in a scaling function basis. This representation is sufficiently general to include the widely used approximation schemes like wavelets, splines and Fourier series representation. We derive a closed form ex ...

SampTA2001

An Exact Method for Computing the Area Moments of Wavelet and Spline Curves

Michaël Unser, Thierry Blu, Mathews Jacob

We present a method for the exact computation of the moments of a region bounded by a curve represented by a scaling function or wavelet basis. Using Green's Theorem, we show that the computation of the area moments is equivalent to applying a suitable mul ...

IEEE2001