On some optimization techniques in image reconstruction from projections

Yair Censor; Gabor T. Herman

doi:10.1016/0168-9274(87)90028-6

On some optimization techniques in image reconstruction from projections

Yair Censor, Gabor T. Herman

Department of Mathematics

Research output: Contribution to journal › Article › 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 paper we present several special-purpose optimization techniques which have been recently developed as reconstruction algorithms. The emphasis of the discussion is on recent developments and open problems.

Original language	English
Pages (from-to)	365-391
Number of pages	27
Journal	Applied Numerical Mathematics
Volume	3
Issue number	5
DOIs	https://doi.org/10.1016/0168-9274(87)90028-6
State	Published - Oct 1987

Bibliographical note

Funding Information:
Work on this paper was begun while Yair Censor was visiting the Medical Image Processing Group (MIPG) at the Department of Radiology, Hospital of the University of Pennsylvania in Philadelphia in February 1985 and completed during a second visit in September 1986. Our research is supported by NIH grant HL28438. We gratefully acknowledge fruitful discussions with Tommy Elfving, Arnold Lent, and Robert M. Lewitt.

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1016/0168-9274(87)90028-6

Cite this

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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 paper we present several special-purpose optimization techniques which have been recently developed as reconstruction algorithms. The emphasis of the discussion is on recent developments and open problems.

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 paper we present several special-purpose optimization techniques which have been recently developed as reconstruction algorithms. The emphasis of the discussion is on recent developments and open problems.

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On some optimization techniques in image reconstruction from projections

Abstract

Bibliographical note

ASJC Scopus subject areas

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