Publications related to Harmonic Spline Series Representation of Scaling Functions

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Domain-Informed Spline Interpolation

Dimitri Nestor Alice Van De Ville, Hamid Behjat, Zafer Dogan

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a single homogeneous domain. In contrast, many naturally occurring signals lie on an inhomogeneous domain, such as brain activity associated to different brain ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Compactly-Supported Smooth Interpolators for Shape Modeling with Varying Resolution

Michaël Unser, Julien René Pierre Fageot, Pablo Garcia-Amorena Garcia, Daniel Andreas Schmitter, Anaïs Laure Marie-Thérèse Badoual

In applications that involve interactive curve and surface modeling, the intuitive manipulation of shapes is crucial. For instance, user interaction is facilitated if a geometrical object can be manipulated through control points that interpolate the shape ...

2017

Multiresolution Subdivision Snakes

Michaël Unser, Daniel Andreas Schmitter, Virginie Sophie Uhlmann, Anaïs Laure Marie-Thérèse Badoual

We present a new family of snakes that satisfy the property of multiresolution by exploiting subdivision schemes. We show in a generic way how to construct such snakes based on an admissible subdivision mask. We derive the necessary energy formulations and ...

2017

An automated baseline correction protocol for infrared spectra of atmospheric aerosols collected on polytetrafluoroethylene (Teflon) filters

Satoshi Takahama, Adela Kuzmiaková

A growing body of research on statistical applications for characterization of atmospheric aerosol Fourier transform infrared (FT-IR) samples collected on polytetrafluoroethylene (PTFE) filters (e.g., Russell et al., 2011; Ruthenburg et al., 2014) and a ri ...

European Geosciences Union2016

Methods of approximation influence aquatic ecosystem metabolism estimates

Janine Rüegg

Aquatic ecologists have recently employed dynamic models to estimate aquatic ecosystem metabolism. All approaches involve numerically solving a differential equation describing dissolved oxygen (DO) dynamics. Although the DO differential equation can be so ...

Association for the Sciences of Limnology and Oceanography2016

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

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

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

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

Harmonic Spline Series Representation of Scaling Functions

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Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

Domain-Informed Spline Interpolation

Compactly-Supported Smooth Interpolators for Shape Modeling with Varying Resolution

Multiresolution Subdivision Snakes

An automated baseline correction protocol for infrared spectra of atmospheric aerosols collected on polytetrafluoroethylene (Teflon) filters

Methods of approximation influence aquatic ecosystem metabolism estimates

Ellipse-Preserving Hermite Interpolation and Subdivision

Statistical Optimality of Hermite Splines

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

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

Domain-Informed Spline Interpolation

An automated baseline correction protocol for infrared spectra of atmospheric aerosols collected on polytetrafluoroethylene (Teflon) filters

Methods of approximation influence aquatic ecosystem metabolism estimates

Compactly-Supported Smooth Interpolators for Shape Modeling with Varying Resolution

Multiresolution Subdivision Snakes

Ellipse-Preserving Hermite Interpolation and Subdivision

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

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

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

Statistical Optimality of Hermite Splines