### 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) |
---|---|

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 |

### Fingerprint

### 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

### Cite this

*Communications in Applied Mathematics and Computational Science*,

*1*(1), 121-131. https://doi.org/10.2140/camcos.2006.1.121

**The fast sinc transform and image reconstruction from nonuniform samples in k-space.** / Greengard, Leslie; Lee, June Yub; Inati, Souheil.

Research output: Contribution to journal › Article

*Communications in Applied Mathematics and Computational Science*, vol. 1, no. 1, pp. 121-131. https://doi.org/10.2140/camcos.2006.1.121

}

TY - JOUR

T1 - The fast sinc transform and image reconstruction from nonuniform samples in k-space

AU - Greengard, Leslie

AU - Lee, June Yub

AU - Inati, Souheil

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Density compensation weights

KW - Fast transform

KW - Fourier analysis

KW - Image reconstruction

KW - Iterative methods

KW - Magnetic resonance imaging (MRI)

KW - Nonuniform fast Fourier transform

KW - Sinc interpolation

UR - http://www.scopus.com/inward/record.url?scp=85015496216&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015496216&partnerID=8YFLogxK

U2 - 10.2140/camcos.2006.1.121

DO - 10.2140/camcos.2006.1.121

M3 - Article

AN - SCOPUS:85015496216

VL - 1

SP - 121

EP - 131

JO - Communications in Applied Mathematics and Computational Science

JF - Communications in Applied Mathematics and Computational Science

SN - 1559-3940

IS - 1

ER -