## Abstract

A number of problems in image reconstruction and image processing can be addressed, in principle, using the sinc kernel. Since the sinc kernel decays slowly, however, it is generally avoided in favor of some more local but less precise choice. In this paper, we describe the fast sinc transform, an algorithm which computes the convolution of arbitrarily spaced data with the sinc kernel in O(N logN) operations, where N denotes the number of data points. We briefly discuss its application to the construction of optimal density compensation weights for Fourier reconstruction and to the iterative approximation of the pseudoinverse of the signal equation in MRI.

Original language | English (US) |
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Pages (from-to) | 121-131 |

Number of pages | 11 |

Journal | Communications in Applied Mathematics and Computational Science |

Volume | 1 |

Issue number | 1 |

DOIs | |

State | Published - 2006 |

## Keywords

- Density compensation weights
- Fast transform
- Fourier analysis
- Image reconstruction
- Iterative methods
- Magnetic resonance imaging (MRI)
- Nonuniform fast Fourier transform
- Sinc interpolation

## ASJC Scopus subject areas

- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics