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A NOTE ON OPTIMAL RECONSTRUCTION OF MAGNETIC RESONANCE IMAGES FROM NON-UNIFORM SAMPLES IN k-SPACE

  • Lee, June-Yub (DEPARTMENT OF MATHEMATICS, EWHA WOMANS UNIVERSITY)
  • Received : 2010.02.08
  • Accepted : 2010.03.05
  • Published : 2010.03.25

Abstract

A goal of Magnetic Resonance Imaging is reproducing a spatial map of the effective spin density from the measured Fourier coefficients of a specimen. The imaging procedure can be done by inverse Fourier transformation or backward fast Fourier transformation if the data are sampled on a regular grid in frequency space; however, it is still a challenging question how to reconstruct an image from a finite set of Fourier data on irregular points in k-space. In this paper, we describe some mathematical and numerical properties of imaging techniques from non-uniform MR data using the pseudo-inverse or the diagonal-inverse weight matrix. This note is written as an easy guide to readers interested in the non-uniform MRI techniques and it basically follows the ideas given in the paper by Greengard-Lee-Inati [10, 11].

Acknowledgement

Supported by : Korea Research Foundation

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