Publications related to Nearest-neighbor interpolation

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

Elsevier Science Sa2023

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Axel Elie Joseph Séguin

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

EPFL2023

Choreography Controlled (ChoCo) brain MRI artifact generation for labeled motion-corrupted datasets

Michel Kocher, François Lazeyras, Bastien Chopard, Sébastien Courvoisier, Julien Songeon

MRI is a non-invasive medical imaging modality that is sensitive to patient motion, which constitutes a major limitation in most clinical applications. Solutions may arise from the reduction of acquisition times or from motion-correction techniques, either ...

ELSEVIER SCI LTD2022

pyFFS: A Python Library for Fast Fourier Series Computation and Interpolation with GPU Acceleration

Martin Vetterli, Paul Hurley, Eric Bezzam, Sepand Kashani, Matthieu Martin Jean-André Simeoni

Fourier transforms are an often necessary component in many computational tasks, and can be computed efficiently through the fast Fourier transform (FFT) algorithm. However, many applications involve an underlying continuous signal, and a more natural choi ...

SIAM2022

On Linear Interpolation in the Latent Space of Deep Generative Models

Quentin Christian Becker, Mike Yan Michelis

The underlying geometrical structure of the latent space in deep generative models is in most cases not Euclidean, which may lead to biases when comparing interpolation capabilities of two models. Smoothness and plausibility of linear interpolations in lat ...

2021

Computation of "Best" Interpolants in the Lp Sense

Michaël Unser, Pakshal Narendra Bohra

We study a variant of the interpolation problem where the continuously defined solution is regularized by minimizing the L p -norm of its second-order derivative. For this continuous-domain problem, we propose an exact discretization scheme that restricts ...

2020

Characterization of the traces on the boundary of functions in magnetic Sobolev spaces

Hoài-Minh Nguyên

We characterize the trace of magnetic Sobolev spaces defined in a half-space or in a smooth bounded domain in which the magnetic field Ais differentiable and its exterior derivative corresponding to the magnetic field dAis bounded. In particular, we prove ...

2020

Approximation of Non-decaying Signals from Shift-Invariant Subspaces

Michaël Unser, Quy Ha Nguyen

In our recent work, the sampling and reconstruction of non-decaying signals, modeled as members of weighted-L-p spaces, were shown to be stable with an appropriate choice of the generating kernel for the shift-invariant reconstruction space. In this paper, ...

2019

Analysis of Resonances in Periodic Metasurfaces through the Concept of Self-Coupling Mode

Kévin Müller

The concept of self-coupling modes, which are eigen-vectors of the roundtrip matrix, is introduced. I investigate its use for the identification and analysis of the resonances taking place in periodic metasurfaces. It also improves the interpolation of the ...

IEEE2019

Regularity results for rough solutions of the incompressible Euler equations via interpolation methods

Maria Colombo, Luigi Forcella, Luigi De Rosa

Given any solutionuof the Euler equations which is assumed to have some regularity in space-in terms of Besov norms, natural in this context-we show by interpolation methods that it enjoys a corresponding regularity in time and that the associated pressure ...

IOP2019

Domain-Informed Spline Interpolation

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

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

Predicting the reflectivity and colour of metals from first principles

Gianluca Prandini

Gold and copper are the only two elemental metals that show a characteristic colour, due to the presence of a drop in the reflectivity curve inside the visible range. Reflectivities of all other metals are in general high and flat for all visible frequenci ...

EPFL2019

Entropy stable essentially non-oscillatory methods based on RBF reconstructions

Jan Sickmann Hesthaven, Fabian Mönkeberg

To solve hyperbolic conservation laws on general grids we propose to use high-order essentially nonoscillatory methods based on radial basis functions. We introduce an entropy stable arbitrary high-order finite dierence method (RBF-TeCNOp) and an entropy s ...

2019

Low-rank tensor methods for large Markov chains and forward feature selection methods

Francisco Santos Paredes Quartin de Macedo

In the first part of this thesis, we present and compare several approaches for the determination of the steady-state of large-scale Markov chains with an underlying low-rank tensor structure. Such structure is, in our context of interest, associated with ...

EPFL2018

Spatial interpolation of precipitation from multiple rain gauge networks and weather radar data for operational applications in Alpine catchments

Giovanni De Cesare, Javier García Hernández, Bettina Schaefli, Alain Tommy Foehn

Increasing meteorological data availability and quality implies an adaptation of the interpolation methods for data combination. In this paper, we propose a new method to efficiently combine weather radar data with data from two heated rain gauge networks ...

2018

Graph-Based Interpolation for Zooming in 3D Scenes

Pascal Frossard, Pinar Akyazi

In multiview systems, color plus depth format builds 3D representations of scenes within which the users can freely navigate by changing their viewpoints. In this paper we present a framework for view synthesis when the user requests an arbitrary viewpoint ...

2017

Spatial Coupling as a Proof Technique and Three Applications

Rüdiger Urbanke, Nicolas Macris, Andrei Giurgiu

The aim of this paper is to show that spatial coupling can be viewed not only as a means to build better graphical models, but also as a tool to better understand uncoupled models. The starting point is the observation that some asymptotic properties of gr ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Heuristic strategies for the approximation of stability factors in quadratically nonlinear parametrized PDEs

Andrea Manzoni, Federico Negri

In this paper we present some heuristic strategies to compute rapid and reliable approximations to stability factors in nonlinear, inf-sup stable parametrized PDEs. The efficient evaluation of these quantities is crucial for the rapid construction of a pos ...

Springer Verlag2015

A Rescaled Localized Radial Basis Function Interpolation On Non-Cartesian And Nonconforming Grids

Alfio Quarteroni, Simone Deparis, Davide Forti

In this paper we propose a rescaled localized radial basis function (RL-RBF) interpolation method, based on the use of compactly supported radial basis functions. Starting from the classical RBF interpolation technique, we introduce a rescaling that allows ...

Siam Publications2014

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