Publications related to On the Continuous Steering of the Scale of Tight Wavelet Frames

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

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

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

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

Multiscale analysis of high resolution digital elevation models using the wavelet transform

Michaël Kalbermatten

At the end of the nineties the emergence of high resolution (1 m) digital elevation models (DEMs) settled the context of high precision geomorphological analysis. These new elevation models permitted to reveal structures that remained heretofore undetectab ...

EPFL2010

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Michaël Unser, Kunal Narayan Chaudhury

We propose an amplitude-phase representation of the dual-tree complex wavelet transform (DT-ℂWT) which provides an intuitive interpretation of the associated complex wavelet coefficients. The representation, in particular, is based on the shifting action o ...

SPIE2009

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

Michaël Unser, Kunal Narayan Chaudhury

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions-the B-spline factorization theorem. In particular, starting from well-localized sc ...

IEEE2009

On the Continuous Steering of the Scale of Tight Wavelet Frames

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

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

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

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

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

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

Decay Properties of Riesz Transforms and Steerable Wavelets

Multiscale analysis of high resolution digital elevation models using the wavelet transform

Gabor Wavelet Analysis and the Fractional Hilbert Transform

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

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

Multiscale analysis of high resolution digital elevation models using the wavelet transform

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

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

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

Gabor Wavelet Analysis and the Fractional Hilbert Transform

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

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

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

Decay Properties of Riesz Transforms and Steerable Wavelets