Publications related to Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Gabor Wavelet Analysis and the Fractional Hilbert Transform

We propose an amplitude-phase representation of the dual-tree complex wavelet transform (DT-ℂWT) which provides an intuitive interpretation of the associated complex wavelet coefficients. The representation, in particular, is based on the shifting action o ...

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

The Fractional Hilbert Transform and Dual-Tree Gabor-Like Wavelet Analysis

Michaël Unser, Kunal Narayan Chaudhury

We provide an amplitude-phase representation of the dual-tree complex wavelet transform by extending the fixed quadrature relationship of the dual-tree wavelets to arbitrary phase-shifts using the fractional Hilbert transform (fHT). The fHT is a generaliza ...

IEEE2009

The Fractional Hilbert Transform And Dual-Tree Gabor-Like Wavelet Analysis

Michaël Unser, Kunal Narayan Chaudhury

We provide an amplitude-phase representation of the dual-tree complex wavelet transform by extending the fixed quadrature relationship of the dual-tree wavelets to arbitrary phase-shifts using the fractional Hilbert transform. (fHT). The fHT is a generaliz ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

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

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

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

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

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

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Gabor Wavelet Analysis and the Fractional Hilbert Transform

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

The Fractional Hilbert Transform and Dual-Tree Gabor-Like Wavelet Analysis

The Fractional Hilbert Transform And Dual-Tree Gabor-Like Wavelet Analysis

The Monogenic Riesz-Laplace Wavelet Transform

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

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

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

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

Gabor Wavelet Analysis and the Fractional Hilbert Transform

The Monogenic Riesz-Laplace Wavelet Transform

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

The Fractional Hilbert Transform and Dual-Tree Gabor-Like Wavelet Analysis

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

The Fractional Hilbert Transform And Dual-Tree Gabor-Like Wavelet Analysis

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

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

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