Publications related to Basis function

Elimination of ringing artifacts by finite-element projection in FFT-based homogenization

Micromechanical homogenization is often carried out with Fourier-accelerated methods that are prone to ringing artifacts. We here generalize the compatibility projection introduced by Vond.rejc et al. (2014) [24] beyond the Fourier basis. In particular, we ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Function Integration, Reconstruction And Approximation Using Rank-1 Lattices

Fabio Nobile, Giovanni Migliorati

We consider rank-1 lattices for integration and reconstruction of functions with series expansion supported on a finite index set. We explore the connection between the periodic Fourier space and the non-periodic cosine space and Chebyshev space, via tent ...

2021

Wavelet-Fourier CORSING techniques for multidimensional advection-diffusion-reaction equations

Fabio Nobile, Simone Brugiapaglia

We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection–diffusion–reaction equations based on the COmpRessed SolvING (CORSING) paradigm. Combining the Petrov–Galerkin technique with the compressed ...

2021

Fourier movement primitives: an approach for learning rhythmic robot skills from demonstrations

Sylvain Calinon, Thibaut Antoine Kulak

Whether in factory or household scenarios, rhythmic movements play a crucial role in many daily-life tasks. In this paper we propose a Fourier movement primitive (FMP) representation to learn such type of skills from human demonstrations. Our approach take ...

2020

TV-based reconstruction of periodic functions

Matthieu Martin Jean-André Simeoni, Julien René Pierre Fageot

We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking the form of a sum ...

IOP PUBLISHING LTD2020

Coupling non-conforming discretizations of PDEs by spectral approximation of the Lagrange multiplier space

Simone Deparis, Luca Pegolotti, Antonio Iubatti

This work focuses on the development of a non-conforming method for the coupling of PDEs based on weakly imposed transmission conditions: the continuity of the global solution is enforced by a finite number of Lagrange multipliers defined over the interfac ...

2019

Measurement of Displacement and Its Derivatives from a Phase Fringe Pattern

Pramod Rastogi, Rishikesh Dilip Kulkarni

Noting the fact that the phase and phase derivatives carry the information on the mechanical deformation in optical interferometric measurements techniques, we propose a noise robust fringe analysis technique for the simultaneous estimation of unwrapped ph ...

SPRINGER INTERNATIONAL PUBLISHING AG2019

Fourier interpolation on the real line

Maryna Viazovska

In this paper we construct an explicit interpolation formula for Schwartz functions on the real line. The formula expresses the value of a function at any given point in terms of the values of the function and its Fourier transform on the set {0,+/- 1,+/- ...

2019

Closed fringe demodulation using phase decomposition by Fourier basis functions

Pramod Rastogi, Rishikesh Dilip Kulkarni

We report a new technique for the demodulation of a closed fringe pattern by representing the phase as a weighted linear combination of a certain number of linearly independent Fourier basis functions in a given row/column at a time. A state space model is ...

2016

Simultaneous estimation of phase and its pth order derivatives

Pramod Rastogi, Rishikesh Dilip Kulkarni

One unaddressed challenge in optical metrology has been the measurement of higher order derivatives of rough specimens subjected to loading. In this paper, we investigate an approach that allows for the simultaneous estimation of the phase and its higher o ...

2016

Design of Steerable Wavelets to Detect Multifold Junctions

Michaël Unser, Cédric René Jean Vonesch, Zsuzsanna Püspöki, Virginie Sophie Uhlmann

We propose a framework for the detection of junctions in images. Although the detection of edges and key points is a well examined and described area, the multiscale detection of junction centers, especially for odd orders, poses a challenge in pattern ana ...

IEEE2015

Operator-Like Wavelet Bases of $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Michaël Unser, Ildar Khalidov, John Paul Ward

The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction follows from a s ...

Springer US2013

Benefits of consistency in image denoising with steerable wavelets

Michaël Unser, Emrah Bostan, Ulugbek Kamilov, Bugra Tekin

The steerable wavelet transform is a redundant image representation with the remarkable property that its basis functions can be adaptively rotated to a desired orientation. This makes the transform well-suited to the design of wavelet-based algorithms app ...

2013

Can Localization Microscopy Benefit From Approximation Theory?

Michaël Unser, Cédric René Jean Vonesch, Hagay Kirshner

We introduce a general and computationally efficient approach to 3-D localization microscopy. The main idea is to construct a continuous-domain representation of the PSF by expanding it in a polynomial B-spline basis. This allows us to fit the PSF to the d ...

IEEE2013

Universal and efficient compressed sensing by spread spectrum and application to realistic Fourier imaging techniques

Pierre Vandergheynst, Yves Wiaux, Rémi Gribonval, Gilles Puy

We advocate a compressed sensing strategy that consists of multiplying the signal of interest by a wide bandwidth modulation before projection onto randomly selected vectors of an orthonormal basis. Firstly, in a digital setting with random modulation, con ...

Institute of Electrical and Electronics Engineers2012

Early detection, warnings, weak signals and seeds of change: A turbulent domain of futures studies

Pierre Rossel

This paper marks a milestone in a six year research cycle on weak signal analysis and early detection issues in futures studies. While providing a broad view and discussing a variety of contributions on this topic, the aim of this article is to offer a mor ...

2012

Groebner Basis Methods for Multichannel Sampling with Unknown Offsets

Martin Vetterli, Luciano Sbaiz, Patrick Vandewalle

In multichannel sampling, several sets of sub-Nyquist sampled signal values are acquired. The offsets between the sets are unknown, and have to be resolved, just like the parameters of the signal itself. This problem is nonlinear in the offsets, but linear ...

Elsevier2008

Polyharmonic Smoothing Splines and the Multidimensional Wiener Filtering of Fractal-Like Signals

Michaël Unser, Dimitri Nestor Alice Van De Ville

Motivated by the fractal-like behavior of natural images, we develop a smoothing technique that uses a regularization functional which is a fractional iterate of the Laplacian. This type of functional was initially introduced by Duchon for the approximatio ...

IEEE2006

Directionlets: Anisotropic Multidirectional representation with separable filtering

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensio ...

2006