Mathematical foundations of computed tomography
Abstract
Along with a review of some of the mathematical foundations of computed tomography, the article contains new results on derivation of reconstruction formulas in a general setting encompassing all standard formulas; discussion and examples of the role of the point spread function with recipes for producing suitable ones; formulas for, and examples of, the reconstruction of certain functions of the attenuation coefficient, e.g., sharpened versions of it, some of them with the property that reconstruction at a point requires only the attenuation along rays meeting a small neighborhood of the point.
 Publication:

Applied Optics
 Pub Date:
 December 1985
 DOI:
 10.1364/AO.24.003950
 Bibcode:
 1985ApOpt..24.3950S
 Keywords:

 Computer Aided Tomography;
 Image Reconstruction;
 Numerical Analysis;
 Point Spread Functions;
 Attenuation Coefficients;
 Fourier Transformation;
 Singular Integral Equations;
 Theorem Proving;
 X Rays;
 Instrumentation and Photography;
 TOMOGRAPHY;
 IMAGE RECONSTRUCTION