Publications related to Gabor Wavelet Analysis and the Fractional Hilbert Transform

Self-Similar Random Vector Fields and Their Wavelet Analysis

This paper is concerned with the mathematical characterization and wavelet analysis of self-similar random vector fields. The study consists of two main parts: the construction of random vector models on the basis of their invariance under coordinate trans ...

SPIE2009

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

Michaël Unser, Dimitri Nestor Alice Van De Ville

Based on the class of complex gradient-Laplace operators, we show the design of a non-separable two-dimensional wavelet basis from a single and analytically defined generator wavelet function. The wavelet decomposition is implemented by an efficient FFT-ba ...

SPIE2009

Hydrological model performance and parameter estimation in the wavelet-domain

Bettina Schaefli

This paper proposes a method for rainfall-runoff model calibration and performance analysis in the wavelet-domain by fitting the estimated wavelet-power spectrum (a representation of the time-varying frequency content of a time series) of a simulated disch ...

European Geosciences Union2009

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

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Michaël Unser, Dimitri Nestor Alice Van De Ville

A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer ad ...

Institute of Electrical and Electronics Engineers2008

A fast thresholded landweber algorithm for general wavelet bases: Application to 3D deconvolution microscopy

Michaël Unser, Cédric René Jean Vonesch

Wavelet-domain l(1)-regularization is a promising approach to deconvolution. The corresponding variational problem can be solved using a "thresholded Landweber" (TL) algorithm. While this iterative procedure is simple to implement, it is known to converge ...

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

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

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

A Fast Thresholded Landweber Algorithm for General Wavelet Bases: Application to 3D Deconvolution Microscopy

Michaël Unser, Cédric René Jean Vonesch

Wavelet-domain

ℓ _{ 1 }

-regularization is a promising approach to deconvolution. The corresponding variational problem can be solved using a “thresholded Landweber” (TL) algorithm. While this iterative procedure is simple to implement, it is known to ...

IEEE2008

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Dimitri Nestor Alice Van De Ville

We present multiresolution spaces of complex rotation-covariant functions, deployed on the 2-D hexagonal lattice. The designed wavelets, which are complex-valued, provide an important phase information for image analysis, which is missing in the discrete w ...

SPIE2007

Gabor Wavelet Analysis and the Fractional Hilbert Transform

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Self-Similar Random Vector Fields and Their Wavelet Analysis

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

Hydrological model performance and parameter estimation in the wavelet-domain

The Monogenic Riesz-Laplace Wavelet Transform

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

A fast thresholded landweber algorithm for general wavelet bases: Application to 3D deconvolution microscopy

Shift-Invariant Spaces from Rotation-Covariant Functions

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

A Fast Thresholded Landweber Algorithm for General Wavelet Bases: Application to 3D Deconvolution Microscopy

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

The Monogenic Riesz-Laplace Wavelet Transform

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

A fast thresholded landweber algorithm for general wavelet bases: Application to 3D deconvolution microscopy

Self-Similar Random Vector Fields and Their Wavelet Analysis

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

Hydrological model performance and parameter estimation in the wavelet-domain

A Fast Thresholded Landweber Algorithm for General Wavelet Bases: Application to 3D Deconvolution Microscopy

Shift-Invariant Spaces from Rotation-Covariant Functions

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis