Iterative Methods for Image Deblurring

This tutorial paper discusses the use of iterative restoration algorithms for the removal of linear blurs from photographic Images which may also be assumed to be degraded by pointwise nonlineariries such as film saturation and additive noise. lterative algorithms are particularly attractive for this application because they allow for the incorporation of various types of prior knowledge about the class of feasible solutions, because they can be used to remove nonstationary blurs, and because they are fairly robust with respect to errors in the approximation of the blurring operator. Special attention is given to the problem of convergence of the algorithms, and classical solutions such as inverse filters, Wiener filters, and constrained least-squares filters are shown to be limiting solutions of variations of the iterations. Regularization is introduced as a means for preventing the excessive noise magnification that is typically associated with ill-conditioned inverse problems such as the deblurring problem, and it is shown that noise effects can be minimized by terminating the algorithms aftera finite number of iterations. The role and choice of constraints on the class of feasible solutions are also discussed. Ringing artifacts are common with most image restoration methods. It is shown that these artifacts can be significantly reduced both by using constraints and also by making the algorithms spatially adaptive. Some variations on the basic iterations that accelerate the rate of convergence are discussed and numerous examples are presented.