Publications related to Fractional Derivatives, Splines and Tomography

Statistical Optimality of Hermite Splines

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Harshit Gupta

Hermite splines are commonly used for interpolating data when samples of the derivative are available, in a scheme called Hermite interpolation. Assuming a suitable statistical model, we demonstrate that this method is actually optimal for reconstructing r ...

IEEE2015

Ellipse-Preserving Hermite Interpolation and Subdivision

Michaël Unser

We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve with the ability t ...

Elsevier2015

Interior Tomography Using 1D Generalized Total Variation. Part I: Mathematical Foundation

Michaël Unser, John Paul Ward

Motivated by the interior tomography problem, we propose a method for exact reconstruction of a region of interest of a function from its local Radon transform in any number of dimensions. Our aim is to verify the feasibility of a one-dimensional reconstru ...

Siam Publications2015

VENUS-LEVIS and its spline-Fourier interpolation of 3D toroidal magnetic field representation for guiding-centre and full-orbit simulations of charged energetic particles

Jonathan Graves, Wilfred Anthony Cooper, David Pfefferlé, Cyril Misev

Curvilinear guiding-centre drift and full-orbit equations of motion are presented as implemented in the code{VENUS-LEVIS} code. A dedicated interpolation scheme based on Fourier reconstruction in the toroidal and poloidal direction and cubic spline in the ...

Elsevier2014

Snakes with Tangent-Based Control and Energies for Bioimage Analysis

Michaël Unser, Ricard Delgado Gonzalo, Virginie Sophie Uhlmann

We propose a novel active contour for the analysis of filament-like structures and boundaries—features that traditional snakes based on closed curves have difficulties to delineate. Our method relies on a parametric representation of an open curve involvin ...

IEEE2014

Cardinal Hermite Exponential Splines: Theoretical Insights and Applications to Active Contours

Michaël Unser, Virginie Sophie Uhlmann

Cardinal Hermite exponential spline functions are a generalization of the classical cardinal Hermite polynomial splines. In this work we consider the 4-dimensional space

ε _{ 4 }

= {1, x,

e ^{ \alpha x }

,

e ^{ -\alpha x }

} with α ∈ $ ℝ ^{ + } ...

SMAI-SIGMA2014

Iterative FBP For Improved Reconstruction Of X-Ray Differential Phase-Contrast Tomograms

Michaël Unser, Cédric René Jean Vonesch, Peter Modregger, Masih Nilchian, Marco Stampanoni

X-ray differential phase-contrast tomography is a recently-developed modality for the imaging of low-contrast biological samples. Its mathematical model is based on the first derivative of the Radon transform and the images, in practice, are reconstructed ...

IEEE2013

Linear Interpolation Of Biomedical Images Using A Data-Adaptive Kernel

Michaël Unser, John Paul Ward, Aurélien Bourquard, Hagay Kirshner

In this work, we propose a continuous-domain stochastic model that can be applied to image data. This model is autoregressive, and accounts for Gaussian-type as well as for non-Gaussian-type innovations. In order to estimate the corresponding parameters fr ...

IEEE2013

Interpolating point spread function anisotropy

Frédéric Courbin, Georges Meylan, Marc Gentile

Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit fro ...

Edp Sciences S A2013

Thin film bulk acoustic wave resonators tuning from first principles

Alexander Tagantsev, Alexander Kvasov

Being important for the antiresonance frequency tuning of tunable thin Film Bulk Acoustic wave Resonators (FBARs), the non-linear electrostrictive coefficient was for the first time calculated for BaTiO3 and SrTiO3 using ab initio methods. Further, taking ...

American Institute of Physics2013

Fractional Derivatives, Splines and Tomography

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Statistical Optimality of Hermite Splines

Ellipse-Preserving Hermite Interpolation and Subdivision

Interior Tomography Using 1D Generalized Total Variation. Part I: Mathematical Foundation

VENUS-LEVIS and its spline-Fourier interpolation of 3D toroidal magnetic field representation for guiding-centre and full-orbit simulations of charged energetic particles

Snakes with Tangent-Based Control and Energies for Bioimage Analysis

Cardinal Hermite Exponential Splines: Theoretical Insights and Applications to Active Contours

Iterative FBP For Improved Reconstruction Of X-Ray Differential Phase-Contrast Tomograms

Linear Interpolation Of Biomedical Images Using A Data-Adaptive Kernel

Interpolating point spread function anisotropy

Thin film bulk acoustic wave resonators tuning from first principles

Snakes with Tangent-Based Control and Energies for Bioimage Analysis

Cardinal Hermite Exponential Splines: Theoretical Insights and Applications to Active Contours

Linear Interpolation Of Biomedical Images Using A Data-Adaptive Kernel

Ellipse-Preserving Hermite Interpolation and Subdivision

Statistical Optimality of Hermite Splines

Interior Tomography Using 1D Generalized Total Variation. Part I: Mathematical Foundation

VENUS-LEVIS and its spline-Fourier interpolation of 3D toroidal magnetic field representation for guiding-centre and full-orbit simulations of charged energetic particles

Iterative FBP For Improved Reconstruction Of X-Ray Differential Phase-Contrast Tomograms

Thin film bulk acoustic wave resonators tuning from first principles

Interpolating point spread function anisotropy