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Structured matrices and unconstrained rational interpolation problems

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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 ...

IEEE2007

Head Related Transfer Functions Interpolation Considering Acoustics

Martin Vetterli, Christof Faller, Luciano Sbaiz, Thibaut Ajdler

We are proposing an interpolation technique for head related transfer functions (HRTFs). For deriving the algorithm we study the dual problem where sound is emitted from the listener’s ear and the generated sound field is recorded along a circular array of ...

2005

Linear Interpolation Revitalized

Michaël Unser, Philippe Thévenaz, Thierry Blu

We present a simple, original method to improve piecewise-linear interpolation with uniform knots: we shift the sampling knots by a fixed amount, while enforcing the interpolation property. We determine the theoretical optimal shift that maximizes the qual ...

IEEE2004

Interpolation of Signals by Generalized Piecewise-Linear Multiple Generators

Michaël Unser, Thierry Blu

This paper presents an interpolation method based on shifted versions of two piecewise linear generators, which provides approximation order 2 like usual piecewise-linear interpolation; i.e., this method is able to represent the constant and the ramp exact ...

IEEE2003

Multiwavelet-Like Bases for High Quality Image Interpolation

Michaël Unser, Thierry Blu

We present a simple but generalized interpolation method for digital images that uses multiwavelet-like basis functions. Most of interpolation methods uses only one symmetric basis function; for example, standard and shifted piecewise-linear interpolations ...

SPIE2003

How a Simple Shift Can Significantly Improve the Performance of Linear Interpolation

Michaël Unser, Philippe Thévenaz, Thierry Blu

We present a simple, original method to improve piecewise linear interpolation with uniform knots: We shift the sampling knots by a fixed amount, while enforcing the interpolation property. Thanks to a theoretical analysis, we determine the optimal shift t ...

IEEE2002

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

Scattered data interpolation methods for electronic imaging systems: a survey

Isaac Amidror

Numerous problems in electronic imaging systems involve the need to interpolate from irregularly spaced data. One example is the calibration of color input/output devices with respect to a common intermediate objective color space, such as XYZ or L* ...

2002

New anisotropic a priori error estimates

Luca Formaggia

We prove a priori anisotropic estimates for the L2 and H1 interpolation error on linear finite elements. The full information about the mapping from a reference element is employed to separate the contribution to the elemental error c ...

2001

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