Publications related to Wavelets on the 2-Hyperboloid

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

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

Stereographic Wavelet Frames on the Sphere

Pierre Vandergheynst, Laurent Jacques, Iva Bogdanova Vandergheynst

In this paper we exploit the Continuous Wavelet Transform (CWT) on the two dimensional sphere, introduced previously by two of us, to build associated Discrete Wavelet Frames. We first explore half-continuous frames, i.e., frames where the position remains ...

2005

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

Exponential-Spline Wavelet Bases

Michaël Unser, Ildar Khalidov

We build a multiresolution analysis based on shift-invariant exponential B-spline spaces. We construct the basis functions for these spaces and for their orthogonal complements. This yields a new family of wavelet-like basis functions of

L _{ 2 }

, wit ...

IEEE2005

Correspondence principle between spherical and Euclidean wavelets

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

Wavelets on the sphere are reintroduced and further developed independently of the original group theoretic formalism, in an equivalent, but more straightforward approach. These developments are motivated by the interest of the scale-space analysis of the ...

2005

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

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

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

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

Wiley-Liss2004

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

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

Wavelets on the 2-Hyperboloid

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

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Stereographic Wavelet Frames on the Sphere

Generalized L-Spline Wavelet Bases

Exponential-Spline Wavelet Bases

Correspondence principle between spherical and Euclidean wavelets

Generalized Biorthogonal Daubechies Wavelets

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

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

Discrete Wavelet Frames on the Sphere

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Stereographic Wavelet Frames on the Sphere

Correspondence principle between spherical and Euclidean wavelets

Generalized Biorthogonal Daubechies Wavelets

Exponential-Spline Wavelet Bases

Discrete Wavelet Frames on the Sphere

Generalized L-Spline Wavelet Bases

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

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