J. Opt. Soc. Amer. 73, pp. 1501-1509 (1983)

Bayesian approach to limited-angle reconstruction in computed tomography

Kenneth M. Hanson and George W. Wechsung
Los Alamos National Laboratory


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 nonsta- tionary 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.

Keywords: Bayesian methods, use of a priori information, null space, limited-angle tomographic reconstruction, Fit and Iterative Reconstruction, FAIR

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