research-article

A fast algorithm for convolution integrals with space and time variant kernels

Authors:

Jost von HardenbergAuthors Info & Claims

Journal of Computational Physics, Volume 216, Issue 1

Pages 326 - 336

https://doi.org/10.1016/j.jcp.2005.12.003

Published: 20 July 2006 Publication History

Abstract

Mathematical models in many fields of the physical sciences involve nonlocal terms which are formally similar to convolution integrals. We show that it is possible to approximate a particular class of such integrals, which by themselves are not convolutions, as a linear combination of convolution integrals, allowing for their efficient numerical computation as an O ( N log N ) process.

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Cited By

Peng YSun QDun XWetzstein GHeidrich WHeide F(2019)Learned large field-of-view imaging with thin-plate opticsACM Transactions on Graphics10.1145/3355089.335652638:6(1-14)Online publication date: 8-Nov-2019
https://dl.acm.org/doi/10.1145/3355089.3356526
Escande PWeiss P(2017)Approximation of Integral Operators Using Product-Convolution ExpansionsJournal of Mathematical Imaging and Vision10.1007/s10851-017-0714-858:3(333-348)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.1007/s10851-017-0714-8
Denis LThiébaut ESoulez FBecker JMourya R(2015)Fast Approximations of Shift-Variant BlurInternational Journal of Computer Vision10.1007/s11263-015-0817-x115:3(253-278)Online publication date: 1-Dec-2015
https://dl.acm.org/doi/10.1007/s11263-015-0817-x

Index Terms

A fast algorithm for convolution integrals with space and time variant kernels
1. Mathematics of computing
  1. Mathematical analysis
    1. Integral equations
    2. Numerical analysis
      1. Numerical differentiation
2. Theory of computation
  1. Design and analysis of algorithms

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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 216, Issue 1

20 July 2006

405 pages

ISSN:0021-9991

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Copyright © Elsevier Inc.

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Academic Press Professional, Inc.

United States

Publication History

Published: 20 July 2006

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Cited By

Peng YSun QDun XWetzstein GHeidrich WHeide F(2019)Learned large field-of-view imaging with thin-plate opticsACM Transactions on Graphics10.1145/3355089.335652638:6(1-14)Online publication date: 8-Nov-2019
https://dl.acm.org/doi/10.1145/3355089.3356526
Escande PWeiss P(2017)Approximation of Integral Operators Using Product-Convolution ExpansionsJournal of Mathematical Imaging and Vision10.1007/s10851-017-0714-858:3(333-348)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.1007/s10851-017-0714-8
Denis LThiébaut ESoulez FBecker JMourya R(2015)Fast Approximations of Shift-Variant BlurInternational Journal of Computer Vision10.1007/s11263-015-0817-x115:3(253-278)Online publication date: 1-Dec-2015
https://dl.acm.org/doi/10.1007/s11263-015-0817-x

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