Publications related to Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

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

Utilization of wavelet-based damage-sensitive features for structural damage assessment of steel braced frames

Dimitrios Lignos, Seong-Hoon Hwang

Rapid structural damage assessment methodologies for engineered facilities are essential in order to properly allocate and ensure efficient use of emergency rescue forces, minimize business interruption and perform effective repairs in damaged infrastructu ...

EMPA2017

Multidimensional Lévy White Noise in Weighted Besov Spaces

Michaël Unser, Julien René Pierre Fageot, Alireza Fallah

In this paper, we study the Besov regularity of a general d-dimensional Lévy white noise. More precisely, we describe new sample paths properties of a given noise in terms of weighted Besov spaces. In particular, we characterize the smoothness and integrab ...

Elsevier2017

Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames

Michaël Unser, Virginie Sophie Uhlmann, Pedram Pad

A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this paper, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the ...

IEEE2016

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

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

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

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

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

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Wavelet analysis of the Besov regularity of Levy white noise

Utilization of wavelet-based damage-sensitive features for structural damage assessment of steel braced frames

Multidimensional Lévy White Noise in Weighted Besov Spaces

Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames

Wavelet Statistics of Sparse and Self-Similar Images

Wavelets: on the virtues and applications of the mathematical microscope

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

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

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

Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames

Multidimensional Lévy White Noise in Weighted Besov Spaces

Utilization of wavelet-based damage-sensitive features for structural damage assessment of steel braced frames

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

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

Wavelets: on the virtues and applications of the mathematical microscope

Wavelet Statistics of Sparse and Self-Similar Images

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

Wavelet analysis of the Besov regularity of Levy white noise

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