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Related Experiment Videos

Interpolation revisited.

P Thévenaz1, T Blu, M Unser

  • 1Swiss Federal Institute of Technology, Lausanne.

IEEE Transactions on Medical Imaging
|October 31, 2000
PubMed
Summary
This summary is machine-generated.

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This study introduces generalized interpolation, using non-interpolating basis functions with prefiltering to reduce artifacts in interpolation and resampling. Splines offer a tunable method for artifact control without significant performance costs.

Area of Science:

  • Signal Processing
  • Numerical Analysis
  • Approximation Theory

Background:

  • Traditional interpolation methods rely on specific basis functions, often leading to artifacts.
  • The choice of basis functions significantly impacts the accuracy of interpolation and resampling.
  • Understanding approximation order is crucial for minimizing interpolation errors.

Purpose of the Study:

  • To provide a unified analysis of interpolation and resampling techniques based on approximation theory.
  • To investigate the role of basis functions in interpolation and resampling accuracy.
  • To introduce and analyze a novel approach termed 'generalized interpolation'.

Main Methods:

  • Analysis of interpolation and resampling through the lens of approximation theory.

Related Experiment Videos

  • Investigation of basis function properties, particularly their approximation order.
  • Application of a decomposition theorem relating basis functions to B-splines.
  • Experimental validation of proposed methods.

    • Main Results:

    • Non-interpolating basis functions, when used with prefiltering (generalized interpolation), outperform traditional interpolating functions.
    • The approximation order of basis functions is critical for limiting interpolation artifacts.
    • Spline-based functions provide a tunable and computationally efficient way to manage artifacts.

    Conclusions:

    • Generalized interpolation offers a superior approach to traditional interpolation for resampling and signal processing tasks.
    • Basis function selection and approximation order are key factors in achieving high-fidelity interpolation.
    • Spline-based methods present a practical and effective solution for artifact reduction in interpolation.