Inversion of incomplete spectral data using support information with an application to magnetic resonance imaging

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Abstract

In this paper we discuss an imaging method when the object has known support and its spatial Fourier transform is only known on a certain k-space undersampled pattern. The simple conjugate gradient least squares algorithm applied to the corresponding truncated Fourier transform equation produces reconstructions that are basically of a similar quality as reconstructions obtained by solving a standard compressed sensing problem in which support information is not taken into account. Connections with previous one-dimensional approaches are highlighted and the performance of the method for two-and three-dimensional simulated and measured incomplete spectral data sets is illustrated. Possible extensions of the method are also briefly discussed.

Original languageEnglish
Article number055006
Pages (from-to)1-13
Number of pages13
JournalJournal of Physics Communications
Volume5
Issue number5
DOIs
Publication statusPublished - 2021

Keywords

  • Compressed sensing
  • Image reconstruction
  • Incomplete spectral data
  • Low-field MRI
  • Magnetic resonance imaging (MRI)
  • Support information

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