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Concept

Pseudo-differential operator

Related publications (26)

Operator-like wavelets with application to functional magnetic resonance imaging

Ildar Khalidov

We introduce a new class of wavelets that behave like a given differential operator L. Our construction is inspired by the derivative-like behavior of classical wavelets. Within our framework, the wavelet coefficients of a signal y are the samples of a smo ...

EPFL2009

Inversion de Fourier ponctuelle

Emanuel Enrico Seifert

Let f be an integrable function on RN, a a point in RN and B a complex number. If the mean value of f on the sphere of centre a and radius r tends to B when r tends to 0, we show that the Fourier integral at a of f is summable to B in Cesàro means of order ...

EPFL2007

Self-Similarity: Part I—Splines and Operators

Michaël Unser, Thierry Blu

The central theme of this pair of papers (Parts I and II in this issue) is self-similarity, which is used as a bridge for connecting splines and fractals. The first part of the investigation is deterministic, and the context is that of L-splines; these are ...

IEEE2007

From Differential Equations to the Construction of New Wavelet-Like Bases

Michaël Unser, Ildar Khalidov

In this paper, an approach is introduced based on differential operators to construct wavelet-like basis functions. Given a differential operator L with rational transfer function, elementary building blocks are obtained that are shifted replicates of the ...

IEEE2006

Direct Numerical Simulation in a Lid-Driven Cubical Cavity at High Reynolds Number by a Chebyshev Spectral Method

Emmanuel Leriche

Direct numerical simulation of the flow in a lid-driven cubicalcavity has been carried out at high Reynolds numbers (based on the maximum velocity on the lid), between 12'000 and 22'000. An efficient Chebyshev spectral method has been implemented for the s ...

Springer, Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com2006

Cardinal Exponential Splines: Part I—Theory and Filtering Algorithms

Michaël Unser, Thierry Blu

Causal exponentials play a fundamental role in classical system theory. Starting from those elementary building blocks, we propose a complete and self-contained signal processing formulation of exponential splines defined on a uniform grid. We specify the ...

IEEE2005

Related publications (26)