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

Merel L. de Leeuw den Bouter; Peter M. van den Berg; Rob F. Remis

doi:10.1088/2399-6528/abfd45

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

Merel L. de Leeuw den Bouter, Peter M. van den Berg, Rob F. Remis

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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 language	English
Article number	055006
Pages (from-to)	1-13
Number of pages	13
Journal	Journal of Physics Communications
Volume	5
Issue number	5
DOIs	https://doi.org/10.1088/2399-6528/abfd45
Publication status	Published - 2021

Keywords

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

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10.1088/2399-6528/abfd45

de_Leeuw_den_Bouter_2021_J._Phys._Commun._5_055006(1)Final published version, 1.39 MBLicence: CC BY

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AU - van den Berg, Peter M.

AU - Remis, Rob F.

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AB - 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.

KW - Compressed sensing

KW - Image reconstruction

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KW - Low-field MRI

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

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