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

• Published in: Journal of physics communications Vol. 5; no. 5; pp. 55006 - 55018
• Main Authors: de Leeuw den Bouter, Merel L, van den Berg, Peter M, Remis, Rob F
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.05.2021
• Subjects: compressed sensing; Fourier transforms; image reconstruction; incomplete spectral data; low-field MRI; magnetic resonance imaging (MRI); support information
• ISSN: 2399-6528; 2399-6528
• DOI: 10.1088/2399-6528/abfd45

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.