Inversion of incomplete spectral data using support information with an application to magnetic resonance imaging
Merel L. de Leeuw den Bouter (TU Delft - Numerical Analysis)
Peter M. van den Berg (TU Delft - ImPhys/Medical Imaging)
R. F. Remis (TU Delft - Signal Processing Systems)
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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.
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