Cardiac magnetic resonance imaging by retrospective gating: mathematical modelling and reconstruction algorithms
J.B.T.M. Roerdink and M. Zwaan. Cardiac magnetic resonance imaging by retrospective gating: mathematical modelling and reconstruction algorithms. Euro. Jnl of Applied Mathematics 4, 1993, pp. 241-270.
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.
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