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

Harmonic Singular Integrals and Steerable Wavelets in $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Here we present a method of constructing steerable wavelet frames in

L _{ 2 }

(\mathbb{R} ^{ d }

) that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the nee ...

Elsevier2014

Wavelets: on the virtues and applications of the mathematical microscope

Michaël Unser

The paper provides a short introduction to wavelets and discusses their main applications in microscopy and biological imaging. ...

Wiley-Blackwell2014

Decay Properties of Riesz Transforms and Steerable Wavelets

Michaël Unser, John Paul Ward, Kunal Narayan Chaudhury

The Riesz transform is a natural multidimensional extension of the Hilbert transform, and it has been the object of study for many years due to its nice mathematical properties. More recently, the Riesz transform and its variants have been used to construc ...

Siam Publications2013

A wavelet analysis for the X-ray absorption spectra of molecules

Majed Chergui, Ursula Röthlisberger, Ivano Tavernelli, Thomas James Penfold, Amal El Nahhas, Marco Eli Reinhard

We present a Wavelet transform analysis for the X-ray absorption spectra of molecules. In contrast to the traditionally used Fourier transform approach, this analysis yields a 2D correlation plot in both R- and k-space. As a consequence, it is possible to ...

American Institute of Physics2013

S2LET: A code to perform fast wavelet analysis on the sphere

Pierre Vandergheynst, Yves Wiaux, Jason Douglas McEwen

We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are con- structed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended features of signals ...

2013

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

Michaël Unser

We introduce a complete parameterization of the family of two-dimensional steerable wavelets that are polar-separable in the Fourier domain under the constraint of self-reversibility. These wavelets are constructed by multiorder generalized Riesz transform ...

Siam Publications2013

On The Optimality Of Operator-Like Wavelets For Sparse Ar(1) Processes

Michaël Unser, Pedram Pad

Sinusoidal transforms such as the DCT are known to be optimal-that is, asymptotically equivalent to the Karhunen-Loeve transform (KLT)-for the representation of Gaussian stationary processes, including the classical AR(1) processes. While the KLT remains a ...

Ieee2013

On the Optimality of Operator-Like Wavelets for Sparse AR(1) Processes

Michaël Unser, Pedram Pad

Sinusoidal transforms such as the DCT are known to be optimal—that is, asymptotically equivalent to the Karhunen-Loève transform (KLT)—for the representation of Gaussian stationary processes, including the classical AR(1) processes. While the KLT remains ...

IEEE2013

On the Sparsity of Wavelet Coefficients for Signals on Graphs

Pierre Vandergheynst, Benjamin Ricaud, David Shuman

A number of new localized, multiscale transforms have recently been introduced to analyze data residing on weighted graphs. In signal processing tasks such as regularization and compression, much of the power of classical wavelets on the real line is deriv ...

Spie-Int Soc Optical Engineering2013

Sparse image reconstruction on the sphere: implications of a new sampling theorem

Jean-Philippe Thiran, Pierre Vandergheynst, Dimitri Nestor Alice Van De Ville, Yves Wiaux, Gilles Puy, Jason Douglas McEwen

A new sampling theorem on the sphere has been developed recently, reducing the number of samples required to represent a band-limited signal by a factor of two for equiangular sampling schemes. For signals sparse in a spatially localised measure, such as i ...

Institute of Electrical and Electronics Engineers2013

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

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Harmonic Singular Integrals and Steerable Wavelets in $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Wavelets: on the virtues and applications of the mathematical microscope

Decay Properties of Riesz Transforms and Steerable Wavelets

A wavelet analysis for the X-ray absorption spectra of molecules

S2LET: A code to perform fast wavelet analysis on the sphere

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

On The Optimality Of Operator-Like Wavelets For Sparse Ar(1) Processes

On the Optimality of Operator-Like Wavelets for Sparse AR(1) Processes

On the Sparsity of Wavelet Coefficients for Signals on Graphs

Sparse image reconstruction on the sphere: implications of a new sampling theorem

On the Optimality of Operator-Like Wavelets for Sparse AR(1) Processes

Decay Properties of Riesz Transforms and Steerable Wavelets

A wavelet analysis for the X-ray absorption spectra of molecules

Harmonic Singular Integrals and Steerable Wavelets in $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

On The Optimality Of Operator-Like Wavelets For Sparse Ar(1) Processes

S2LET: A code to perform fast wavelet analysis on the sphere

Wavelets: on the virtues and applications of the mathematical microscope

Sparse image reconstruction on the sphere: implications of a new sampling theorem

On the Sparsity of Wavelet Coefficients for Signals on Graphs