Publications related to Wavelet Steerability and the Higher-Order Riesz Transform

Fast Detection and Refined Scale Estimation Using Complex Isotropic Wavelets

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

The dyadic scaling in the discrete wavelet transform can lead to a loss of precision, in comparison to the computationally unrealistic continuous wavelet transform. To overcome this obstacle, we propose a novel method to locally scale wavelets between dyad ...

IEEE2015

Optimized Kaiser-Bessel Window Functions for Computed Tomography

Michaël Unser, Cédric René Jean Vonesch, John Paul Ward, Masih Nilchian

Kaiser-Bessel window functions are frequently used to discretize tomographic problems because they have two desirable properties: 1) their short support leads to a low computational cost and 2) their rotational symmetry makes their imaging transform indepe ...

Ieee-Inst Electrical Electronics Engineers Inc2015

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

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

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

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

Wavelet Steerability and the Higher-Order Riesz Transform

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Fast Detection and Refined Scale Estimation Using Complex Isotropic Wavelets

Optimized Kaiser-Bessel Window Functions for Computed Tomography

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

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

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

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 } $ )

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

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

Fast Detection and Refined Scale Estimation Using Complex Isotropic Wavelets

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

Decay Properties of Riesz Transforms and Steerable Wavelets

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

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

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

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

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

Optimized Kaiser-Bessel Window Functions for Computed Tomography

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