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Algebraic Reconstruction Techniques

  • Timothy G. Feeman
Chapter
Part of the Springer Undergraduate Texts in Mathematics and Technology book series (SUMAT)

Abstract

To this point, we have studied how Fourier transform methods are used in image reconstruction. This is the approach taken in the seminal work of Cormack [13] and used in the algorithms of today’s CT scan machines. However, the first CT scanner, designed in the late 1960 s by Godfrey Hounsfield, used an approach grounded in linear algebra and matrix theory to generate an image from the machine readings. Algorithms that adopt this point of view are known as algebraic reconstruction techniques, or ART, for short. In this chapter, we look at a few basic mathematical elements of ART.

Keywords

Normal Equation Relaxation Parameter Feasibility Problem Algebraic Reconstruction Technique Image Grid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York 2010

Authors and Affiliations

  1. 1.Department of Mathematical SciencesVillanova UniversityVillanovaUSA

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