Three methods for reconstructing objects from x rays: A comparative study

Three algorithms for reconstructing objects from their projections are compared. Such algorithms are useful in locating the position and shape of tumors from X rays taken of a patient and in finding the structure of viruses and macromolecules from electron micrographs. The comparisons are carried out from the point of view of overall nearness of the reconstruction to the original, resolution in fine detail, and cost. Detailed comparisons are carried out by the use of experiments on six representative pictures which are reconstructed by all three techniques. The performance of the algorithms is investigated both in the absence and presence of noise. The results of the experiments are discussed with special attention to the applicability of the methods. The three methods under investigation are: (i) an improved version of the direct additive method of Gordon, Bender, and Herman, as proposed by Herman, Lent, and Rowland; (ii) the convolution method of Bracewell and Riddle with a generalization of the implementation proposed by Ramachandran and Lakshminarayanan; (iii) a generalized version of the simultaneous iterative technique of Gilbert.