Mathematical Aspects of Image Reconstruction from Projections

Martin D. Altschuler; Yair Censor; Gabor T. Herman; Arnold Lent; Robert M. Lewitt; Sargur N. Srihari; Heang Tuy; Jayaram K. Udupa

doi:10.1016/B978-0-444-86325-6.50012-6

Mathematical Aspects of Image Reconstruction from Projections

Martin D. Altschuler, Yair Censor, Gabor T. Herman, Arnold Lent, Robert M. Lewitt, Sargur N. Srihari, Heang Tuy, Jayaram K. Udupa

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

Image reconstruction from projections is a procedure of extreme usefulness in many scientific and medical fields. In particular, it has revolutionized diagnostic radiology in the last decade. The mathematical essence of the procedure is the estimation and presentation of a real-valued function of several variables from approximate values of a finite number of its line integrals. In this article we survey some of the mathematics associated with practical image reconstruction from projections. The topics dealt with include reconstruction from incomplete data, techniques based on optimization theory, the fully three-dimensional problem, and the display of reconstructions.

Original language	English
Title of host publication	Progress in Pattern Recognition
Editors	Laveen N. KANAL, Azriel ROSENFELD
Place of Publication	Amsterdam
Publisher	North-Holland Publ Co
Pages	323-375
Number of pages	53
ISBN (Print)	978-0-444-86325-6
DOIs	https://doi.org/10.1016/B978-0-444-86325-6.50012-6
State	Published - 1981

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10.1016/B978-0-444-86325-6.50012-6

https://www.sciencedirect.com/science/article/pii/B9780444863256500126

Cite this

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title = "Mathematical Aspects of Image Reconstruction from Projections",

abstract = "Image reconstruction from projections is a procedure of extreme usefulness in many scientific and medical fields. In particular, it has revolutionized diagnostic radiology in the last decade. The mathematical essence of the procedure is the estimation and presentation of a real-valued function of several variables from approximate values of a finite number of its line integrals. In this article we survey some of the mathematics associated with practical image reconstruction from projections. The topics dealt with include reconstruction from incomplete data, techniques based on optimization theory, the fully three-dimensional problem, and the display of reconstructions.",

author = "Altschuler, {Martin D.} and Yair Censor and Herman, {Gabor T.} and Arnold Lent and Lewitt, {Robert M.} and Srihari, {Sargur N.} and Heang Tuy and Udupa, {Jayaram K.}",

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T1 - Mathematical Aspects of Image Reconstruction from Projections

AU - Altschuler, Martin D.

AU - Censor, Yair

AU - Herman, Gabor T.

AU - Lent, Arnold

AU - Lewitt, Robert M.

AU - Srihari, Sargur N.

AU - Tuy, Heang

AU - Udupa, Jayaram K.

PY - 1981

Y1 - 1981

N2 - Image reconstruction from projections is a procedure of extreme usefulness in many scientific and medical fields. In particular, it has revolutionized diagnostic radiology in the last decade. The mathematical essence of the procedure is the estimation and presentation of a real-valued function of several variables from approximate values of a finite number of its line integrals. In this article we survey some of the mathematics associated with practical image reconstruction from projections. The topics dealt with include reconstruction from incomplete data, techniques based on optimization theory, the fully three-dimensional problem, and the display of reconstructions.

AB - Image reconstruction from projections is a procedure of extreme usefulness in many scientific and medical fields. In particular, it has revolutionized diagnostic radiology in the last decade. The mathematical essence of the procedure is the estimation and presentation of a real-valued function of several variables from approximate values of a finite number of its line integrals. In this article we survey some of the mathematics associated with practical image reconstruction from projections. The topics dealt with include reconstruction from incomplete data, techniques based on optimization theory, the fully three-dimensional problem, and the display of reconstructions.

U2 - 10.1016/B978-0-444-86325-6.50012-6

DO - 10.1016/B978-0-444-86325-6.50012-6

M3 - Chapter

SN - 978-0-444-86325-6

SP - 323

EP - 375

BT - Progress in Pattern Recognition

A2 - KANAL, Laveen N.

A2 - ROSENFELD, Azriel

PB - North-Holland Publ Co

CY - Amsterdam

ER -

Mathematical Aspects of Image Reconstruction from Projections

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