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RF pulse design using the inverse scattering transform

M H Buonocore1

  • 1Division of Diagnostic Radiology, UC Davis Medical Center, Sacramento 95817.

Magnetic Resonance in Medicine
|April 1, 1993
PubMed
Summary
This summary is machine-generated.

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The inverse scattering transform (IST) unifies three numerical algorithms for deriving radiofrequency (RF) pulses. These methods, including finite rank kernel, layer stripping, and Shinnar-Le Roux (SLR), are shown to be equivalent when applied to spin system spectra.

Area of Science:

  • Physics
  • Applied Mathematics
  • Signal Processing

Background:

  • The inverse scattering transform (IST) is a mathematical framework used to design radiofrequency (RF) pulses for magnetic resonance.
  • Several numerical algorithms exist for generating these RF pulses, but their interrelationships are not always clear.

Purpose of the Study:

  • To review and demonstrate the unified derivation of three distinct numerical algorithms from the IST.
  • To establish the equivalence of these algorithms under different spectral representations.

Main Methods:

  • The study analyzes the mathematical underpinnings of the finite rank kernel method, layer stripping, and the Shinnar-Le Roux (SLR) algorithm.
  • It shows how each algorithm arises from the IST by making specific assumptions about the form of the continuous spectra (rational, Fourier series, or ratios of Fourier series).

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Main Results:

  • All three algorithms—finite rank kernel, layer stripping, and SLR—are demonstrated to be derivable from the IST.
  • The equivalence of these algorithms is shown through interconversion between rational, series, and ratio of series spectral forms.

Conclusions:

  • The inverse scattering transform provides a unifying theoretical basis for several RF pulse design algorithms.
  • These algorithms, despite their different origins, generate RF pulses with comparable performance characteristics.