Limited-Angle Image Reconstruction in Non-Destructive Evaluation

Abstract

The practice and the theory of image reconstruction in conventional x-ray computerized tomography (CT) is briefly reviewed. Limited-angle CT is introduced where it is shown that scanning in a restricted angular range results in missing information, which in term causes the problem to become underdetermined. The use of generally available a priori information can compensate for the missing information and therefore improve the reconstructed image. An efficient iterative transform algorithm which utilizes the a priori information in conjunction with the limited-angle x-ray data to reconstruct the object is described. The object is transformed back and forth between the object space and the projection space, being corrected by the a priori information in the object space, and the limited-angle known projections in the projection space. The use of the convex hull of the object in image reconstruction is intorduced, and the procedure for the construction of the hull from the x-ray data detailed. The use of more specific a priori information is shown to further improve the reconstructed image. Finally, the applications of limited-angle image reconstruction to the reduction of scan time and dosage in fan beam scanning, image improvement in conventional digital tomography, and ultrasonic flaw characterization are discussed.