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

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

Calderón–Zygmund estimates and non-uniformly elliptic operators

Maria Colombo

We consider a class of non-uniformly nonlinear elliptic equations whose model is given by -div(vertical bar Du vertical bar(p-2)Du a(x) vertical bar Du vertical bar(q-2)Du) = -div(vertical bar F vertical bar Fp-2 a(x)vertical bar F vertical bar Fq-2) where ...

2016

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

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

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

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 Local Wall Stiffness Drop in Steel-Lined Pressure Tunnels and Shafts of Hydroelectric Power Plants Using Steep Pressure Wave Excitation and Wavelet Decomposition

Anton Schleiss, Fadi Hachem

A new monitoring approach for detecting, locating, and quantifying structurally weak reaches of steel-lined pressure tunnels and shafts is presented. These reaches arise from local deterioration of the backfill concrete and the rock mass surrounding the li ...

2012

Optimally Localized Wavelets and Smoothing Kernels

Kunal Narayan Chaudhury

It is well-known that the Gaussian functions and, more generally, their modulations-translations (the Gabor functions) have the unique property of being optimally localized in space and frequency in the sense of Heisenberg's uncertainty principle. In this ...

EPFL2011

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

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

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On the Continuous Steering of the Scale of Tight Wavelet Frames

Calderón–Zygmund estimates and non-uniformly elliptic operators

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

Decay Properties of Riesz Transforms and Steerable Wavelets

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

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

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

Detection of Local Wall Stiffness Drop in Steel-Lined Pressure Tunnels and Shafts of Hydroelectric Power Plants Using Steep Pressure Wave Excitation and Wavelet Decomposition

Optimally Localized Wavelets and Smoothing Kernels

Wavelet Steerability and the Higher-Order Riesz Transform

On the Continuous Steering of the Scale of Tight Wavelet Frames

Calderón–Zygmund estimates and non-uniformly elliptic operators

Decay Properties of Riesz Transforms and Steerable Wavelets

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

Wavelet Steerability and the Higher-Order Riesz Transform

Optimally Localized Wavelets and Smoothing Kernels

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

Detection of Local Wall Stiffness Drop in Steel-Lined Pressure Tunnels and Shafts of Hydroelectric Power Plants Using Steep Pressure Wave Excitation and Wavelet Decomposition

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

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