Publications related to Haar wavelet

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Michaël Unser, Julien René Pierre Fageot, Emrah Bostan

We study the statistics of wavelet coefficients of non-Gaussian images, focusing mainly on the behaviour at coarse scales. We assume that an image can be whitened by a fractional Laplacian operator, which is consistent with an

∥ω∥ ^{ -\gamma }

spectral ...

IEEE2014

Influence of atrial substrate on local capture induced by rapid pacing of atrial fibrillation

Jean-Marc Vesin, Vincent Jacquemet, Alexandru Rusu

Preliminary studies showed that the septum area was the only location allowing local capture of both the atria during rapid pacing of atrial fibrillation (AF) from a single site. The present model-based study investigated the influence of atrial substrate ...

Oxford University Press2014

On the computation of directional scale-discretized wavelet transforms on the sphere

Pierre Vandergheynst, Yves Wiaux, Jason Douglas McEwen

We review scale-discretized wavelets on the sphere, which are directional and allow one to probe oriented struc- ture in data defined on the sphere. Furthermore, scale-discretized wavelets allow in practice the exact synthesis of a signal from its wavelet ...

SPIE2013

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

Operator-Like Wavelet Bases of L-2(R-d)

Michaël Unser, John Paul Ward, Ildar Khalidov

The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction follows from a s ...

Springer Birkhauser2013

Operator-Like Wavelet Bases of $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Michaël Unser, John Paul Ward, Ildar Khalidov

The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction follows from a s ...

Springer US2013

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

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

Fast continuous Fourier and Haar transforms of rectilinear polygons from very-large-scale integration layouts

Paul Hurley, Robin Scheibler, Amina Chebira

We propose two new fast algorithms for the computation of the continuous Fourier series and the continuous Haar transform of rectilinear polygons such as those of mask layouts in optical lithography. These algorithms outperform their discrete counterparts ...

2013

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Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Influence of atrial substrate on local capture induced by rapid pacing of atrial fibrillation

On the computation of directional scale-discretized wavelet transforms on the sphere

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

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

Operator-Like Wavelet Bases of L-2(R-d)

Operator-Like Wavelet Bases of $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

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

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

Fast continuous Fourier and Haar transforms of rectilinear polygons from very-large-scale integration layouts

Influence of atrial substrate on local capture induced by rapid pacing of atrial fibrillation

Operator-Like Wavelet Bases of L-2(R-d)

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

On the computation of directional scale-discretized wavelet transforms on the sphere

Operator-Like Wavelet Bases of $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

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

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

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

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Fast continuous Fourier and Haar transforms of rectilinear polygons from very-large-scale integration layouts