Publications related to Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

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

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

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

Michaël Unser, Dimitri Nestor Alice Van De Ville, Ildar Khalidov

Tomographic reconstruction from positron emission tomography (PET) data is an ill-posed problem that requires regularization. An attractive approach is to impose an

\ell_{ 1 }

-regularization constraint, which favors sparse solutions in the wavelet dom ...

Institute of Electrical and Electronics Engineers2008

Shift-Invariant Spaces from Rotation-Covariant Functions

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

We consider shift-invariant multiresolution spaces generated by rotation-covariant functions ρ in

\mathbb{R}^{ 2 }

. To construct corresponding scaling and wavelet functions, ρ has to be localized with an appropriate multiplier, such that the localized ...

Elsevier2008

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our aim in this paper is to tighten the link between wavelets, some classical image-processing operators, and David Marr's theory of early vision. The cornerstone of our approach is a new complex wavelet basis that behaves like a smoothed version of the Gr ...

Institute of Electrical and Electronics Engineers2008

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

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

The “Marr wavelet pyramid” is a wavelet decomposition that implements a multiscale version of the complex gradient-Laplace operator. It is closely linked to a multiresolution analysis of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) and it has a fast filterbank im ...

EURASIP2008

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

The continous wavelet transform on conic sections

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We review the coherent state or group-theoretical 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 ...

2008

Sparsity-based Source Separation with Scale-Discretized Steerable Wavelets

Pierre Vandergheynst, Yves Wiaux

In this talk, we discuss the issue of source separation in a signal on the sphere or on the plane, relying on the sparsity of one signal component in a scale-discretized steerable wavelet basis. The steerability of wavelets allows to probe in detail the lo ...

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

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

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

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

Shift-Invariant Spaces from Rotation-Covariant Functions

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

The continuous wavelet transform on conic sections

The continous wavelet transform on conic sections

Sparsity-based Source Separation with Scale-Discretized Steerable Wavelets

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

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

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

Sparsity-based Source Separation with Scale-Discretized Steerable Wavelets

The continuous wavelet transform on conic sections

The continous wavelet transform on conic sections

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

Shift-Invariant Spaces from Rotation-Covariant Functions

Dynamic PET Reconstruction Using Wavelet Regularization with Adapted Basis Functions

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

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