Publications related to Statistical wavelet analysis of functional images of the brain

Wavelet Statistics of Sparse and Self-Similar Images

Michaël Unser, Julien René Pierre Fageot, Emrah Bostan

It is well documented that natural images are compressible in wavelet bases and tend to exhibit fractal properties. In this paper, we investigate statistical models that mimic these behaviors. We then use our models to make predictions on the statistics of ...

Siam Publications2015

Optimal Isotropic Wavelets for Localized Tight Frame Representations

Michaël Unser, John Paul Ward, Pedram Pad

In this letter, we aim to identify the optimal isotropic mother wavelet for a given spatial dimension based on a localization criterion. Within the framework of the calculus of variations, we specify an Euler-Lagrange equation for this problem, and we find ...

IEEE2015

Modeling the Importance of Faces in Natural Images

Sabine Süsstrunk, Cheryl Shaulya Lau, Appu Shaji, Gökhan Yildirim, Bin Jin

In this work we study the varying importance of faces in images. Face importance is found to be affected by the size and number of faces present. We collected a dataset of 152 face images with faces in different size and number of faces. We conducted a cro ...

Spie-Int Soc Optical Engineering2015

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

Harmonic singular integrals and steerable wavelets in L-2(R-d)

Michaël Unser, John Paul Ward

Here we present a method of constructing steerable wavelet frames in L-2(R-d) that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the need to more accurately account ...

Academic Press Inc Elsevier Science2014

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

Michaël Unser, John Paul Ward

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

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

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

Statistical wavelet analysis of functional images of the brain

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Wavelet Statistics of Sparse and Self-Similar Images

Optimal Isotropic Wavelets for Localized Tight Frame Representations

Modeling the Importance of Faces in Natural Images

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Harmonic singular integrals and steerable wavelets in L-2(R-d)

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

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

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

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

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

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

Modeling the Importance of Faces in Natural Images

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Harmonic singular integrals and steerable wavelets in L-2(R-d)

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

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

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

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

Wavelet Statistics of Sparse and Self-Similar Images

Optimal Isotropic Wavelets for Localized Tight Frame Representations