Publications related to Wavelet Theory Demystified

Wavelet Transform Analysis of Truncated Fringe Patterns in 3-D Surface Profilometry

Wavelet transform analysis of projected fringe pattern for phase recovery in 3-D shape measurement of objects is investigated. The present communication specifically outlines and evaluates the errors that creep in to the reconstructed profiles when fringe ...

2005

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 Biorthogonal Daubechies Wavelets

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We propose a generalization of the Cohen-Daubechies-Feauveau (CDF) and 9⁄7 biorthogonal wavelet families. This is done within the framework of non-stationary multiresolution analysis, which involves a sequence of embedded approximation spaces generated by ...

SPIE2005

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Michaël Unser, Dimitri Nestor Alice Van De Ville, Daniel Sage

Microscopy imaging often suffers from limited depth-of-focus. However, the specimen can be “optically sectioned” by moving the object along the optical axis; different areas appear in focus in different images. Extended depth-of-focus is a fusion algorithm ...

IEEE2004

Wavelets on the 2-Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We build wavelets on the 2-Hyperboloid. First, we define dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to

SO_0(1,2)

, we define a family of hyperbolic wavelets. The continuous wavelet transform (CW ...

2004

Isotropic-Polyharmonic B-Splines and Wavelets

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

We propose the use of polyharmonic B-splines to build non-separable two-dimensional wavelet bases. The central idea is to base our design on the isotropic polyharmonic B-splines, a new type of polyharmonic B-splines that do converge to a Gaussian as the or ...

IEEE2004

Wavelet and footprint sampling of signals with a finite rate of innovation

Martin Vetterli, Pier Luigi Dragotti

In this paper, we consider classes of not bandlimited signals, namely, streams of Diracs and piecewise polynomial signals, and show that these signals can be sampled and perfectly reconstructed using wavelets as sampling kernel. Due to the multiresolution ...

2004

Extended Depth-of-Field for Color Images in Light Microscopy: Image Fusion and 3D Visualization

Michaël Unser, Dimitri Nestor Alice Van De Ville, Niels Quack, Daniel Sage

Bright-field microscopy suffers from a relatively small depth-of-field. Typically, the specimen’s profile covers a range larger than the depth-of-field, and parts of the specimen that lie outside the object plane appear blurred. The specimen can be ‘scanne ...

2004

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

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

Wavelet Theory Demystified

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Wavelet Transform Analysis of Truncated Fringe Patterns in 3-D Surface Profilometry

Generalized Daubechies Wavelets

Generalized Biorthogonal Daubechies Wavelets

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Wavelets on the 2-Hyperboloid

Isotropic-Polyharmonic B-Splines and Wavelets

Wavelet and footprint sampling of signals with a finite rate of innovation

Extended Depth-of-Field for Color Images in Light Microscopy: Image Fusion and 3D Visualization

Fractional Splines, Wavelet Bases, and Applications

Fractional Wavelets, Derivatives, and Besov Spaces

Generalized Biorthogonal Daubechies Wavelets

Wavelet Transform Analysis of Truncated Fringe Patterns in 3-D Surface Profilometry

Generalized Daubechies Wavelets

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Wavelets on the 2-Hyperboloid

Fractional Wavelets, Derivatives, and Besov Spaces

Extended Depth-of-Field for Color Images in Light Microscopy: Image Fusion and 3D Visualization

Isotropic-Polyharmonic B-Splines and Wavelets

Fractional Splines, Wavelet Bases, and Applications

Wavelet and footprint sampling of signals with a finite rate of innovation