Reconstruction of three-dimensional binary structures from an extremely limited number of cone-beam x-ray projections. Choice of prior

Abstract

A newly developed technique for the three-dimensional x-ray reconstruction of binary images is discussed. It allows one to reduce extremely (about 10-100 times) the number of required projections and views and to suppress the main artifacts. The technique is based upon the solution of an imposed operator equation using special types of functionals, which are also discussed. The steps for its solution provide the zero-level approximation, the computer simulation of the radiographic process and the use of the a priori knowledge about structural features in general form. They give the priority to planar and/or volumetric images in the matrix. The efficiency of corresponding functionals and algorithms is compared to the maximum-likelihood (ML) estimation using both simulated and real radiographic data. The introduced prior functionals are discussed in terms of Markov random fields and Gibbs statistics used for Bayesian image reconstruction with higher-order models as priors.

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