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

Wavelet-Fourier CORSING techniques for multidimensional advection-diffusion-reaction equations

We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection–diffusion–reaction equations based on the COmpRessed SolvING (CORSING) paradigm. Combining the Petrov–Galerkin technique with the compressed ...

2020

Wavelet analysis of the Besov regularity of Levy white noise

Julien René Pierre Fageot, Shayan Aziznejad

We characterize the local smoothness and the asymptotic growth rate of the Levy white noise. We do so by characterizing the weighted Besov spaces in which it is located. We extend known results in two ways. First, we obtain new bounds for the local smoothn ...

2020

On the Continuous Steering of the Scale of Tight Wavelet Frames

Michaël Unser, Daniel Sage, Zsuzsanna Püspöki, John Paul Ward

In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation of steering ste ...

SIAM2016

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

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

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

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

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

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

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Wavelet-Fourier CORSING techniques for multidimensional advection-diffusion-reaction equations

Wavelet analysis of the Besov regularity of Levy white noise

On the Continuous Steering of the Scale of Tight Wavelet Frames

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

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

Wavelets: on the virtues and applications of the mathematical microscope

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

Decay Properties of Riesz Transforms and Steerable Wavelets

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

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

Wavelet-Fourier CORSING techniques for multidimensional advection-diffusion-reaction equations

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

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

On the Continuous Steering of the Scale of Tight Wavelet Frames

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

Wavelet analysis of the Besov regularity of Levy white noise

Decay Properties of Riesz Transforms and Steerable Wavelets

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

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

Wavelets: on the virtues and applications of the mathematical microscope