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