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

Leslie Greengard, June Yub Lee, Souheil Inati

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)121-131
Number of pages11
JournalCommunications in Applied Mathematics and Computational Science
Volume1
Issue number1
DOIs
StatePublished - 2006

Fingerprint

K-space
Image Reconstruction
Image reconstruction
Convolution
Magnetic resonance imaging
Image processing
Transform
kernel
Pseudo-inverse
Image Processing
Decay
Denote
Approximation
Compensation and Redress

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

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

In: Communications in Applied Mathematics and Computational Science, Vol. 1, No. 1, 2006, p. 121-131.

Research output: Contribution to journalArticle

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