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Cardiac magnetic resonance imaging by retrospective gating: mathematical modelling and reconstruction algorithms

Published online by Cambridge University Press:  26 September 2008

J. B. T. M. Roerdink  and
M. Zwaan
J. B. T. M. Roerdink
Affiliation:
Centre for Mathematics and Computer Science, PO Box 4079, 1009 AB Amsterdam, The Netherlands
M. Zwaan
Affiliation:
Centre for Mathematics and Computer Science, PO Box 4079, 1009 AB Amsterdam, The Netherlands
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Abstract

This paper is concerned with some mathematical aspects of magnetic resonance imaging (MRI) of the beating human heart. In particular, we investigate the so-called retrospective gating technique which is a non-triggered technique for data acquisition and reconstruction of (approximately) periodically changing organs like the heart. We formulate the reconstruction problem as a moment problem in a Hilbert space and give the solution method. The stability of the solution is investigated and various error estimates are given. The reconstruction method consists of temporal interpolation followed by spatial Fourier inversion. Different choices for the Hilbert space ℋ of interpolating functions are possible. In particular, we study the case where ℋ is (i) the space of bandlimited functions, or (ii) the space of spline functions of odd degree. The theory is applied to reconstructions from synthetic data as well as real MRI data.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 4 , Issue 3 , September 1993 , pp. 241 - 270
Copyright
Copyright © Cambridge University Press 1993

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