Publication

Fast Computation of Polyharmonic B-Spline Autocorrelation Filters

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu, Yann Barbotin
2008
Journal Articles

Abstract

A fast computational method is given for the Fourier transform of the polyharmonic B-spline autocorrelation sequence in d dimensions. The approximation error is exponentially decaying with the number of terms taken into account. The algorithm improves speed upon a simple truncated-sum approach. Moreover, it is virtually independent of the spline's order. The autocorrelation filter directly serves for various tasks related to polyharmonic splines, such as interpolation, orthonormalization, and wavelet basis design.

Official source

https://infoscience.epfl.ch/entities/publication/e97de68b-54f1-42a6-b93c-765e41aec7e8

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Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu, Yann Barbotin
2008
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/e97de68b-54f1-42a6-b93c-765e41aec7e8

About this result

Related concepts (23)

Fourier transform

In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.

Spline interpolation

In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the values, for example, fitting nine cubic polynomials between each of the pairs of ten points, instead of fitting a single degree-ten polynomial to all of them.

Discrete Fourier transform

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies.

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