Computationally efficient 3-D statistical reconstruction from digitized radiographs

X-ray and γ-ray radiography have been indispensable techniques for materials inspection for many years. Internal structure is typically inferred from radiographs by human evaluation. More precise information is possible if the function of three spatial variables can be estimated directly from the radiographic data. Several mathematical inversion formulae have been derived for deterministic reconstruction from the cone-beam integral projection data represented by the radiographs, but depend on large numbers of measurements for usable reconstructions. Bayesian statistical approaches are more robust to data limitations, and can function usefully in the presence of severe system limitations. The solution of the estimation problem, however, is an formidable numerical challenge, requiring inordinate amounts of computing power and data storage for quality reconstructions. This paper presents techniques for reducing the computation time and storage requirements for iterative approximation from digitized radiographs. Examples of these reconstructions are provided for physical experiments with steel samples imaged on radiographic film