Cone-beam tomography with discrete data sets

Harrison H Barrett, H. Gifford

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

Sufficiency conditions for cone-beam data are well known for the case of continuous data collection along a cone-vertex curve with continuous detectors. These continuous conditions are inadequate for real-world data where discrete vertex geometries and discrete detector arrays are used. The authors present a theoretical formulation of cone-beam tomography with arbitrary discrete arrays of detectors and vertices. The theory models the imaging system as a linear continuous-to-discrete mapping and represents the continuous object exactly as a Fourier series. The reconstruction problem is posed as the estimation of some subset of the Fourier coefficients. The main goal of the theory is to determine which Fourier coefficients can be reliably determined from the data delivered by a specific discrete design. A Fourier component will be well determined by the data if it satisfies two conditions: it makes a strong contribution to the data, and this contribution is relatively independent of the contribution of other Fourier components. To make these considerations precise, the authors introduce a concept called the cross-talk matrix. A diagonal element of this matrix measures the strength of a Fourier component in the data, while an off-diagonal element quantifies the dependence or aliasing of two different components. One reasonable approach to system design is to attempt to make the diagonal elements of this matrix large and the off-diagonal elements small for some set of Fourier components. If this goal can be achieved, simple linear reconstruction algorithms are available for estimating the Fourier coefficients. To illustrate the usefulness of this approach, numerical results on the cross-talk matrix are presented for different discrete geometries derived from a continuous helical vertex orbit, and simulated images reconstructed with two linear algorithms are presented.

Original languageEnglish (US)
Article number012
Pages (from-to)451-476
Number of pages26
JournalPhysics in Medicine and Biology
Volume39
Issue number3
DOIs
StatePublished - 1994

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Tomography
Cones
cones
tomography
apexes
Orbit
Fourier Analysis
Detectors
matrices
detectors
coefficients
Geometry
Fourier series
Set theory
Imaging systems
geometry
Orbits
systems engineering
Systems analysis
set theory

ASJC Scopus subject areas

  • Radiological and Ultrasound Technology
  • Radiology Nuclear Medicine and imaging
  • Physics and Astronomy (miscellaneous)
  • Biomedical Engineering

Cite this

Cone-beam tomography with discrete data sets. / Barrett, Harrison H; Gifford, H.

In: Physics in Medicine and Biology, Vol. 39, No. 3, 012, 1994, p. 451-476.

Research output: Contribution to journalArticle

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