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Computer-assisted proof of kernel inequalities

Related publications (34)

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Short Basis Functions for Constant-Variance Interpolation

Michaël Unser, Philippe Thévenaz, Thierry Blu

An interpolation model is a necessary ingredient of intensity-based registration methods. The properties of such a model depend entirely on its basis function, which has been traditionally characterized by features such as its order of approximation and it ...

SPIE2008

The arcsine law as a universal aging scheme for trap models

Jiri Cerny

We give a general proof of aging for trap models using the arcsine law for stable subordinators. This proof is based on abstract conditions on the potential theory of the underlying graph and on the randomness of the trapping landscape. We apply this proof ...

2008

Regularized interpolation for noisy data

Michaël Unser, Philippe Thévenaz, Sathish Ramani

Interpolation is a vital tool in biomedical signal processing. Although there exists a substantial literature dedicated to noise-free conditions, much less is known in the presence of noise. Here, we document the breakdown of standard interpolation for noi ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2007

Regularized Interpolation for Noisy Data

Michaël Unser, Philippe Thévenaz, Sathish Ramani

IEEE2007

A Light Formulation of the E* Interpolated Path Replanner

Roland Philippsen

The E* algorithm is a path planning method capable of dynamic replanning and user-configurable path cost interpolation, it results in more appropriate paths during gradient descent. The underlying formulation is based on interpreting navigation functions a ...

2006

Acoustic Based Rendering by Interpolation of the Plenacoustic Function

Martin Vetterli, Thibaut Ajdler

We study the spatialization of the sound field in a room, in particular the evolution of room impulse responses as function of their spatial positions. The presented technique allows us to completely characterize the sound field in any arbitrary location i ...

2003

Filter Design for Filtered Back-Projection Guided by the Interpolation Model

Michaël Unser

We consider using spline interpolation to improve the standard filtered back-projection (FBP) tomographic reconstruction algorithm. In particular, we propose to link the design of the filtering operator with the interpolation model that is applied to the s ...

SPIE2002

A Chronology of Interpolation: From Ancient Astronomy to Modern Signal and Image Processing

This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently us ...

IEEE2002

Stable spectral methods on tetrahedral elements

Jan Sickmann Hesthaven

A framework for the construction of stable spectral methods on arbitrary domains with unstructured grids is presented. Although most of the developments are of a general nature, an emphasis is placed on schemes for the solution of partial differential equa ...

SIAM PUBLICATIONS2000

Interpolation Revisited

Michaël Unser, Philippe Thévenaz, Thierry Blu

Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. We show that, contrary to the common belief, those that perform best are ...

IEEE2000