Publications related to Wavelets on the two-sphere and other conic sections

Rotation Invariance and Directional Sensitivity: Spherical Harmonics versus Radiomics Features

Michaël Unser, Julien René Pierre Fageot, John Paul Ward, Adrien Raphaël Depeursinge

We define and investigate the Local Rotation Invariance (LRI) and Directional Sensitivity (DS) of radiomics features. Most of the classical features cannot combine the two properties, which are antagonist in simple designs. We propose texture operators bas ...

SPRINGER INTERNATIONAL PUBLISHING AG2018

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

Wavelet Statistics of Sparse and Self-Similar Images

Michaël Unser, Julien René Pierre Fageot, Emrah Bostan

It is well documented that natural images are compressible in wavelet bases and tend to exhibit fractal properties. In this paper, we investigate statistical models that mimic these behaviors. We then use our models to make predictions on the statistics of ...

Siam Publications2015

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

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

The Effect of Scale on the Applicability of Taylor’s Frozen Turbulence Hypothesis in the Atmospheric Boundary Layer

Valentin Simeonov, Martin Froidevaux, Marc Parlange, Chad Higgins, Nikki Vercauteren, Caitlin Ellen Barry

Taylor’s frozen turbulence hypothesis is the central assumption invoked in most experiments designed to investigate turbulence physics with time resolving sensors. It is also frequently used in theoretical discussions when linking Lagrangian to Eulerian fl ...

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

On the Hilbert Transform of Wavelets

Michaël Unser, Kunal Narayan Chaudhury

A wavelet is a localized function having a prescribed number of vanishing moments. In this correspondence, we provide precise arguments as to why the Hilbert transform of a wavelet is again a wavelet. In particular, we provide sharp estimates of the locali ...

IEEE2011

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Rotation Invariance and Directional Sensitivity: Spherical Harmonics versus Radiomics Features

On the Continuous Steering of the Scale of Tight Wavelet Frames

Wavelet Statistics of Sparse and Self-Similar Images

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

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

The Effect of Scale on the Applicability of Taylor’s Frozen Turbulence Hypothesis in the Atmospheric Boundary Layer

Optimally Localized Wavelets and Smoothing Kernels

On the Hilbert Transform of Wavelets

Rotation Invariance and Directional Sensitivity: Spherical Harmonics versus Radiomics Features

Wavelet Statistics of Sparse and Self-Similar Images

Wavelets: on the virtues and applications of the mathematical microscope

On the Continuous Steering of the Scale of Tight Wavelet Frames

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

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

On the Hilbert Transform of Wavelets

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

Optimally Localized Wavelets and Smoothing Kernels

The Effect of Scale on the Applicability of Taylor’s Frozen Turbulence Hypothesis in the Atmospheric Boundary Layer