EQUIVALENCE OF REGULARIZATION AND TRUNCATED ITERATION IN THE SOLUTION OF ILL-POSED IMAGE-RECONSTRUCTION PROBLEMS

The equivalence of minimum-norm least-squares solutions of systems of linear equations and standard iterative methods of solution is well established. On the other hand, while it is generally understood that truncated iteration is a form of regularization, comparatively few papers have formalized the relationship between direct methods of regularization and truncated iteration. A brief review of such papers is presented. The main result of this paper is to carry this idea one step further and prove that solutions by direct regularization are in fact identical to solutions of a certain type of truncated-iterative method, and conversely. This equivalence is proved by construction for a very general form of regularization method in which the coefficient matrix has full rank and is rectangular. © 1990.