Publications associées à Fresnelets: New Multiresolution Wavelet Bases for Digital Holography

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

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

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

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-value ...

Institute of Electrical and Electronics Engineers2009

The use of wavelet transform for an automated initialization in GPS/MEMS-IMU integration

Jan Skaloud, Adrian Wägli, Heidi Fournier

The main objective of this research is in automating the initialization phase of the MEMS-IMZ/GPS data integration. The motivation for this study is the special case where the before mentioned sensors are worn on a body (e.g. of an athlete) and where the u ...

2009

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

Michaël Unser, Kunal Narayan Chaudhury

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions-the B-spline factorization theorem. In particular, starting from well-localized sc ...

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 generaliza ...

IEEE2009

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

Michaël Unser, Dimitri Nestor Alice Van De Ville, Pouya Dehghani Tafti

In this contribution, we study the notion of affine invariance (specifically, invariance to the shifting, scaling, and rotation of the coordinate system) as a starting point for the development of mathematical tools and approaches useful in the characteriz ...

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 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

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

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

Fresnelets: New Multiresolution Wavelet Bases for Digital Holography

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Gabor Wavelet Analysis and the Fractional Hilbert Transform

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

The use of wavelet transform for an automated initialization in GPS/MEMS-IMU integration

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

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

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

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

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

Shift-Invariant Spaces from Rotation-Covariant Functions

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

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Shift-Invariant Spaces from Rotation-Covariant Functions

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

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

Invariances, Laplacian-Like Wavelet Bases, and the Whitening of Fractal Processes

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

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

The use of wavelet transform for an automated initialization in GPS/MEMS-IMU integration

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