RF pulse design using the inverse scattering transform

Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine
Michael H Buonocore

Abstract

The inverse scattering transform (IST) is a mathematical transformation that can be used to derive RF pulses from functions called continuous spectra describing the final state of the spin system. This paper reviews three seemingly unrelated numerical algorithms that have appeared in the literature, and shows that they are all derivable from the IST. When the continuous spectra are rational, the finite rank kernel method is used to convert the IST to a matrix equation that is easily solved. Another algorithm, equivalent to the so-called "layer stripping" algorithm used in seismology, is derived by assuming that the spectra are Fourier series. Finally, the Shinnar-Le Roux (SLR) algorithm is derived by assuming that the spectra are ratios of Fourier series. With proper interconversion between the rational, series, and ratio of series forms of the continuous spectra, these algorithms generate RF pulses with identical or nearly identical shapes and performance properties, and can be regarded as equivalent.

References

Apr 1, 1992·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·M H Buonocore
Oct 1, 1989·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·M Shinnar, J S Leigh
Feb 1, 1987·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·D Kunz
Jan 1, 1991·IEEE Transactions on Medical Imaging·J PaulyA Macovski

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Citations

Jan 17, 2016·Journal of Magnetic Resonance·Christoph Stefan AignerRudolf Stollberger
Dec 14, 2004·Journal of Magnetic Resonance·Jeremy Magland, Charles L Epstein
Jul 26, 2007·IEEE Transactions on Medical Imaging·Logi VidarssonJohn M Pauly
Nov 24, 2004·IEEE Transactions on Medical Imaging·Jose Luis UlloaPablo Irarrazaval
Jan 3, 2001·Journal of Magnetic Resonance·U Klose, A Raddi
Dec 1, 2000·Journal of Magnetic Resonance·J W Carlson
May 26, 1999·Journal of Magnetic Resonance·Z Xu, A K Chan
Feb 29, 2008·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Dan XuZhi-Pei Liang

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