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Generalized Interpolation: Higher Quality at no Additional Cost

Publications associées (38)

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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

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

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

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

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

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

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

Image Interpolation and Resampling

Michaël Unser, Philippe Thévenaz, Thierry Blu

This chapter presents a survey of interpolation and resampling techniques in the context of exact, separable interpolation of regularly sampled data. In this context, the traditional view of interpolation is to represent an arbitrary continuous function as ...

Academic Press2000

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

Complete Parametrization of Piecewise-Polynomial Interpolators According to Degree, Support, Regularity, and Order

Michaël Unser, Philippe Thévenaz, Thierry Blu

The most essential ingredient of interpolation is its basis function. We have shown in previous papers that this basis need not be necessarily interpolating to achieve good results. On the contrary, several recent studies have confirmed that non-interpolat ...

IEEE2000