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Short Basis Functions for Constant-Variance Interpolation

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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

A Note on Cubic Convolution Interpolation

Michaël Unser

We establish a link between classical osculatory interpolation and modern convolution-based interpolation and use it to show that two well-known cubic convolution schemes are formally equivalent to two osculatory interpolation schemes proposed in the actua ...

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

Why Restrict Ourselves to Compactly Supported Basis Functions?

Michaël Unser, Thierry Blu

Compact support is undoubtedly one of the wavelet properties that is given the greatest weight both in theory and applications. It is usually believed to be essential for two main reasons: (1) to have fast numerical algorithms, and (2) to have good time or ...

SPIE2001

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

Elastic image registration using parametric deformation models

Jan Kybic

The main topic of this thesis is elastic image registration for biomedical applications. We start with an overview and classification of existing registration techniques. We revisit the landmark interpolation which appears in the landmark-based registratio ...

EPFL2001

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

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