Publications related to Wavelets on the 2-Sphere: A Group-Theoretical Approach

The continuous wavelet transform on conic sections

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We review the known construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two- sheeted hyperboloid, emphasizing the similarities between the two cases. Finally we give s ...

2008

Continuous-wavelet transform for fault location in distribution power networks: Definition of mother wavelets inferred from fault originated transients

Mario Paolone

The paper presents a fault location procedure for distribution networks based on the wavelet analysis of the fault-generated traveling waves. In particular, the proposed procedure implements the continuous wavelet analysis applied to the voltage waveforms ...

2008

The Monogenic Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Katarina Balac

We introduce a family of real and complex wavelet bases of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) that are directly linked to the Laplace and Riesz operators. The crucial point is that the family is closed with respect to the Riesz transform which maps a re ...

EURASIP2008

Representation of Radon Shape Diffusions via Hyperspherical Brownian Motion

Victor Panaretos

A framework is introduced for the study of general Radon shape diffusions, that is, shape diffusions induced by projections of randomly rotating shapes. This is done via a convenient representation of unoriented Radon shape diffusions in (unoriented) D.G. ...

2008

Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization

Michaël Unser, Kunal Narayan Chaudhury

We propose a novel method of constructing exact Hilbert transform (HT) pairs of wavelet bases using fractional B-splines and state necessary and sufficient conditions for generating such wavelet pairs. In particular, we demonstrate how HT pairs of biorthog ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

Construction of Hilbert Transform Pairs of Wavelet Bases and Optimal Time-Frequency Localization

Michaël Unser, Kunal Narayan Chaudhury

We propose a novel method of constructing exact Hilbert transform (HT) pairs of wavelet bases using fractional B-splines and state necessary and sufficient conditions for generating such wavelet pairs. In particular, we demonstrate how HT pairs of biorthog ...

IEEE2008

Wavelets on the two-sphere and other conic sections

Pierre Vandergheynst

We review the construction of the continuous wavelet transform (CWT) on the two-sphere by two methods, the group-theoretical approach and the geometrical method based on conformal invariance. Then we discuss the discretization of the spherical CWT, obtaini ...

2007

Continuous Wavelet Transform on the Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

In this paper we build a Continuous Wavelet Transform (CWT) on the upper sheet of the 2-hyperboloid

H_+^2

. First, we define a class of suitable dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to $SO ...

2007

3D Shape Extraction of Human Face in Presence of Facial Hair: A Profilometric Approach

Sai Siva Gorthi

The increasing use of 3D modeling of Human Face in Face Recognition systems, User Interfaces, Graphics , Gaming and the like has made it an area of active study. Majority of the 3D sensors rely on color coded light projection for 3D estimation. Such system ...

2007

WSPM: Wavelet-Based Statistical Parametric Mapping

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

Recently, we have introduced an integrated framework that combines wavelet-based processing with statistical testing in the spatial domain. In this paper, we propose two important enhancements of the framework. First, we revisit the underlying paradigm; i. ...

Elsevier2007

Wavelets on the 2-Sphere: A Group-Theoretical Approach

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The continuous wavelet transform on conic sections

Continuous-wavelet transform for fault location in distribution power networks: Definition of mother wavelets inferred from fault originated transients

The Monogenic Riesz-Laplace Wavelet Transform

Representation of Radon Shape Diffusions via Hyperspherical Brownian Motion

Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization

Construction of Hilbert Transform Pairs of Wavelet Bases and Optimal Time-Frequency Localization

Wavelets on the two-sphere and other conic sections

Continuous Wavelet Transform on the Hyperboloid

3D Shape Extraction of Human Face in Presence of Facial Hair: A Profilometric Approach

WSPM: Wavelet-Based Statistical Parametric Mapping

Representation of Radon Shape Diffusions via Hyperspherical Brownian Motion

WSPM: Wavelet-Based Statistical Parametric Mapping

The continuous wavelet transform on conic sections

Continuous-wavelet transform for fault location in distribution power networks: Definition of mother wavelets inferred from fault originated transients

The Monogenic Riesz-Laplace Wavelet Transform

Continuous Wavelet Transform on the Hyperboloid

Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization

Construction of Hilbert Transform Pairs of Wavelet Bases and Optimal Time-Frequency Localization

Wavelets on the two-sphere and other conic sections

3D Shape Extraction of Human Face in Presence of Facial Hair: A Profilometric Approach