Publications related to Generalizations of the derivative

Analytical approximation for the recession of a sloping aquifer

An approximation is obtained for the recession of a sloping aquifer. The analytical approximation can provide a useful tool to analyze data and obtain physical properties of the aquifer. In contrast to the case of a horizontal aquifer, when plotting the ti ...

American Geophysical Union2014

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Michaël Unser, Julien René Pierre Fageot, Emrah Bostan

We study the statistics of wavelet coefficients of non-Gaussian images, focusing mainly on the behaviour at coarse scales. We assume that an image can be whitened by a fractional Laplacian operator, which is consistent with an

∥ω∥ ^{ -\gamma }

spectral ...

IEEE2014

Transport equation describing fractional Lévy motion of suprathermal ions in TORPEX

Ambrogio Fasoli, Ivo Furno, Paolo Ricci, Kyle Gustafson, Alexandre Dominique Bovet, Matteo Gamarino

Suprathermal ions, created by fusion reactions or by additional heating, will play an important role in burning plasmas such as the ones in ITER or DEMO. Basic plasma experiments, with easy access for diagnostics and well-controlled plasma scenarios, are p ...

Iop Publishing Ltd2014

Enhanced Conversion of Carbohydrates to the Platform Chemical 5-Hydroxymethylfurfural Using Designer Ionic Liquids

Paul Joseph Dyson, Rosario Scopelliti, Gabor Laurenczy, Zhaofu Fei, Ning Yan, Sviatlana Siankevich

5-Hydroxymethylfurfural (HMF) is a key platform chemical that may be obtained from various cellulosic (biomass) derivatives. Previously, it has been shown that ionic liquids (ILs) facilitate the catalytic conversion of glucose into HMF. Herein, we demonstr ...

Wiley-V C H Verlag Gmbh2014

Multiscale Interior Tomography Using 1D Generalized Total Variation

Michaël Unser, John Paul Ward

We propose a method for accurate and fast reconstruction of the interior of a 2D or 3D tomographic image from its incomplete local Radon transform. Unlike the existing interior tomography work with 2D total variation, the proposed algorithm guarantees exac ...

The University of Utah2014

3-D PSF fitting for fluorescence microscopy: implementation and localization application

Michaël Unser, Daniel Sage, François Aguet, Hagay Kirshner

Localization microscopy relies on computationally efficient Gaussian approximations of the point spread function for the calculation of fluorophore positions. Theoretical predictions show that under specific experimental conditions, localization accuracy i ...

Wiley-Blackwell2013

Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves

Boris Buffoni

In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal direction. The proof is ...

Academic Press Inc Elsevier Science2013

Hessian Schatten-Norm Regularization for Linear Inverse Problems

Michaël Unser, John Paul Ward, Stamatios Lefkimmiatis

We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian matrix, which a ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Convex Generalizations of Total Variation Based on the Structure Tensor with Applications to Inverse Problems

Michaël Unser, Stamatios Lefkimmiatis

We introduce a generic convex energy functional that is suitable for both grayscale and vector-valued images. Our functional is based on the eigenvalues of the structure tensor, therefore it penalizes image variation at every point by taking into account t ...

Springer2013

Generalized Flows Satisfying Spatial Boundary Conditions

Boris Buffoni

In a region D in R-2 or R-3, the classical Euler equation for the regular motion of an inviscid and incompressible fluid of constant density is given by partial derivative(t)v + (v . del(x))v = -del(xP), div(x)v = 0, where v(t, x) is the velocity of the pa ...

Birkhäuser-Verlag, Springer2012

Generalizations of the derivative

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Analytical approximation for the recession of a sloping aquifer

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Transport equation describing fractional Lévy motion of suprathermal ions in TORPEX

Enhanced Conversion of Carbohydrates to the Platform Chemical 5-Hydroxymethylfurfural Using Designer Ionic Liquids

Multiscale Interior Tomography Using 1D Generalized Total Variation

3-D PSF fitting for fluorescence microscopy: implementation and localization application

Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves

Hessian Schatten-Norm Regularization for Linear Inverse Problems

Convex Generalizations of Total Variation Based on the Structure Tensor with Applications to Inverse Problems

Generalized Flows Satisfying Spatial Boundary Conditions

Transport equation describing fractional Lévy motion of suprathermal ions in TORPEX

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Enhanced Conversion of Carbohydrates to the Platform Chemical 5-Hydroxymethylfurfural Using Designer Ionic Liquids

Hessian Schatten-Norm Regularization for Linear Inverse Problems

Multiscale Interior Tomography Using 1D Generalized Total Variation

3-D PSF fitting for fluorescence microscopy: implementation and localization application

Convex Generalizations of Total Variation Based on the Structure Tensor with Applications to Inverse Problems

Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves

Generalized Flows Satisfying Spatial Boundary Conditions

Analytical approximation for the recession of a sloping aquifer