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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 73, Iss. 11 — Nov. 1, 1983
  • pp: 1501–1509

Bayesian approach to limited-angle reconstruction in computed tomography

Kenneth M. Hanson and George W. Wecksung  »View Author Affiliations


JOSA, Vol. 73, Issue 11, pp. 1501-1509 (1983)
http://dx.doi.org/10.1364/JOSA.73.001501


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Abstract

An arbitrary source function cannot be determined fully from projection data that are limited in number and range of viewing angle. There exists a null subspace in the Hilbert space of possible source functions about which the available projection measurements provide no information. The null-space components of deterministic solutions are usually zero, giving rise to unavoidable artifacts. It is demonstrated that these artifacts may be reduced by a Bayesian maximum a posteriori (MAP) reconstruction method that permits the use of significant a priori information. Since normal distributions are assumed for the a priori and measurement-error probability densities, the MAP reconstruction method presented here is equivalent to the minimum-variance linear estimator with nonstationary mean and covariance ensemble characterizations. A more comprehensive Bayesian approach is suggested in which the ensemble mean and covariance specifications are adjusted on the basis of the measurements.

© 1983 Optical Society of America

Citation
Kenneth M. Hanson and George W. Wecksung, "Bayesian approach to limited-angle reconstruction in computed tomography," J. Opt. Soc. Am. 73, 1501-1509 (1983)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-73-11-1501


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