Publications related to Wavelets, Filterbanks, and the Karhunen-Loève Transform

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

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

Multi-Lead Wavelet-Based ECG Delineation on a Wearable Embedded Sensor Platform

David Atienza Alonso, Francisco Javier Rincon Vallejos, Nadia Khaled, Nicolas Boichat

This work is dedicated to the sensible optimization and porting of a multi-lead (ML) wavelet-transform (WT)-based electrocardiogram (ECG) wave delineator to a state-of-the-art commercial wearable embedded sensor platform with limited processing and storage ...

2009

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

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

SURE-LET Multichannel Image Denoising: Interscale Orthonormal Wavelet Thresholding

Thierry Blu, Florian Luisier

We propose a vector/matrix extension of our denoising algorithm initially developed for grayscale images, in order to efficiently process multichannel (e.g., color) images. This work follows our recently published SURE-LET approach where the denoising algo ...

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 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

Wavelets, Filterbanks, and the Karhunen-Loève Transform

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

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

Multi-Lead Wavelet-Based ECG Delineation on a Wearable Embedded Sensor Platform

The Monogenic Riesz-Laplace Wavelet Transform

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

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

SURE-LET Multichannel Image Denoising: Interscale Orthonormal Wavelet Thresholding

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

The continous wavelet transform on conic sections

Sparsity-based Source Separation with Scale-Discretized Steerable Wavelets

The Monogenic Riesz-Laplace Wavelet Transform

Multi-Lead Wavelet-Based ECG Delineation on a Wearable Embedded Sensor Platform

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

The continous wavelet transform on conic sections

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

Sparsity-based Source Separation with Scale-Discretized Steerable Wavelets

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

SURE-LET Multichannel Image Denoising: Interscale Orthonormal Wavelet Thresholding

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

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