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Computerized tomography and nuclear magnetic resonance

Journal of Computer Assisted Tomography

|February 1, 1980

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This study presents a numerical algorithm for Radon's 1917 formula, enabling function reconstruction from plane integrals. This method is applicable to imaging nuclear magnetic resonance spin density.

Area of Science:

Mathematics
Image Reconstruction
Medical Imaging

Background:

Johann Radon's 1917 formula provides a theoretical basis for reconstructing functions from integrals over planes in 3D space.
Reconstructing functions from integral data is fundamental in various scientific and engineering fields.

Purpose of the Study:

To develop a simple numerical algorithm for computing Radon's reconstruction formula.
To explore the application of this algorithm in imaging nuclear magnetic resonance (NMR) spin density.

Main Methods:

The study implements a numerical quadrature algorithm to approximate Radon's inversion formula.
The algorithm focuses on efficient computation for practical applications.

Main Results:

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A straightforward algorithm for numerical quadrature of Radon's formula has been developed.
The algorithm is demonstrated to be suitable for reconstructing NMR spin density.

Conclusions:

The developed numerical algorithm offers a practical approach to function reconstruction using Radon's formula.
This method has potential applications in advanced medical imaging techniques like NMR spin density imaging.