Local tomography

Adel Faridani, Erik L. Ritman, Kennan T. Smith

Research output: Contribution to journalArticle

156 Citations (Scopus)

Abstract

Tomography produces the reconstruction of a function f from a large number of line integrals of f. Conventional tomography is a global procedure in that the standard convolution formulas for reconstruction at a single point require the integrals over all lines within some plane containing the point. Local tomography, as introduced initially, produced the reconstruction of the related function Λf, where Λ is the square root of -Δ, the positive Laplace operator. The reconstruction of Λf is local in that reconstruction at a point requires integrals only over lines passing infinitesimally close to the point, and Λf has the same smooth regions and boundaries as f. However, Λf is cupped in regions where f is constant. Λ -1f, also amendable to local reconstruction, is smooth everywhere and contains a counter-up. This article provides a detailed study of the actions of Λ and Λ -1, and shows several examples of what can be achieved with a linear combination. It includes the results of x-ray experiments in which the line integrals are obtained from attenuation measurements on two-dimensional image intensifiers and fluorescent screens, instead of the usual linear detector arrays.

Original languageEnglish (US)
Pages (from-to)459-484
Number of pages26
JournalSIAM Journal on Applied Mathematics
Volume52
Issue number2
StatePublished - Apr 1992
Externally publishedYes

Fingerprint

Tomography
Fluorescent screens
Curvilinear integral
Convolution
Image Intensifier
Detectors
X rays
Line
Positive Operator
Laplace Operator
Square root
Attenuation
Linear Combination
Experiments
Detector
Experiment

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Faridani, A., Ritman, E. L., & Smith, K. T. (1992). Local tomography. SIAM Journal on Applied Mathematics, 52(2), 459-484.

Local tomography. / Faridani, Adel; Ritman, Erik L.; Smith, Kennan T.

In: SIAM Journal on Applied Mathematics, Vol. 52, No. 2, 04.1992, p. 459-484.

Research output: Contribution to journalArticle

Faridani, A, Ritman, EL & Smith, KT 1992, 'Local tomography', SIAM Journal on Applied Mathematics, vol. 52, no. 2, pp. 459-484.
Faridani A, Ritman EL, Smith KT. Local tomography. SIAM Journal on Applied Mathematics. 1992 Apr;52(2):459-484.
Faridani, Adel ; Ritman, Erik L. ; Smith, Kennan T. / Local tomography. In: SIAM Journal on Applied Mathematics. 1992 ; Vol. 52, No. 2. pp. 459-484.
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