Computational considerations of the two-dimensional discrete x-ray transform

Saleem Gregory Zougbi

doi:10.1117/12.18916

1 July 1990 Computational considerations of the two-dimensional discrete x-ray transform

Saleem Gregory Zougbi

Proceedings Volume 1233, Medical Imaging IV: Image Processing; (1990) https://doi.org/10.1117/12.18916
Event: Medical Imaging '90, 1990, Newport Beach, CA, United States

Abstract

If photons are of constant energy and if they are emitted with constant intensity in the body say I then the intensity I of the photons reaching a film is established as I 10 e IS I''(XrY) dx. dy (1) where IA(x is the Xray attenuation coefficient of the medium (tissue or organ) at point (x from the source. An X-''ray transform is defined for a function f(x as i: f(( 1 J'' f( e . f(: ds . dt (2) It is shown that after sampling the discrete form of this transform is N N . ) ''i. nk i i 1 e '' (3) In this paper the computational aspects of this transform are studied and different algorithmic procedures are outlined. Furthermore its application in convolution and filtering is evaluated in medical image processing. Emphasis is placed on the use of residue arithmetic where this transform is used as numbertheoretic. It is compared with other potentially effective transforms as specially applied to medical image processing. 392 / SPIE Vol. 1233 Medical Imaging/V Image Processing (1990)

Citation Download Citation

Saleem Gregory Zougbi "Computational considerations of the two-dimensional discrete x-ray transform", Proc. SPIE 1233, Medical Imaging IV: Image Processing, (1 July 1990); https://doi.org/10.1117/12.18916

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