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

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

On the eigenvalue decay of solutions to operator Lyapunov equations

Daniel Kressner

This paper is concerned with the eigenvalue decay of the solution to operator Lyapunov equations with right-hand sides of finite rank. We show that the kth (generalized) eigenvalue decays exponentially in root k, provided that the involved operator A gener ...

Elsevier Science Bv2014

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

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

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 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

Detection Of Symmetric Junctions In Biological Images Using 2-D Steerable Wavelet Transforms

Michaël Unser, Cédric René Jean Vonesch

We present a method for designing steerable wavelets that can detect local centers of symmetry in images. Based on this design, we then propose an algorithm for estimating the locations and the orientations of M-fold symmetric junctions in biological micro ...

IEEE2013

Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications

Michaël Unser, Aurélien Bourquard, Stamatios Lefkimmiatis

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second- ...

IEEE2012

Wavelet Steerability and the Higher-Order Riesz Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions (d ≥ 2). To that end, we introduce a self-reversible, Nth-order ...

Institute of Electrical and Electronics Engineers2010

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

We introduce a family of elementary singularities that are point-Holder alpha-regular. These singularities are self-similar and are the Green functions of fractional derivative operators; i.e., by suitable fractional differentiation, one retrieves a Dirac ...

Institute of Electrical and Electronics Engineers2010

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

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Statistics of Wavelet Coefficients for Sparse Self-Similar Images

On the eigenvalue decay of solutions to operator Lyapunov equations

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

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

Decay Properties of Riesz Transforms and Steerable Wavelets

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

Detection Of Symmetric Junctions In Biological Images Using 2-D Steerable Wavelet Transforms

Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications

Wavelet Steerability and the Higher-Order Riesz Transform

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

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

Decay Properties of Riesz Transforms and Steerable Wavelets

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

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

On the eigenvalue decay of solutions to operator Lyapunov equations

Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications

Wavelet Steerability and the Higher-Order Riesz Transform

Analytical Footprints: Compact Representation of Elementary Singularities in Wavelet Bases

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Detection Of Symmetric Junctions In Biological Images Using 2-D Steerable Wavelet Transforms