Iterative Image Restoration

Abstract

In the previous chapter we have described the problems involved in solving the ill-conditioned image restoration problem, and we have shown that several classical restoration filters can be classified as Tikhonov-Miller regularized methods. In this chapter we will consider the use of iterative methods in image restoration. Iterative procedures offer the advantage that no matrix inverses need to be implemented, and that additional deterministic constraints can be incorporated into the solution algorithms. Section4.1 introduces the basic iterative restoration algorithm that forms the basis for most of the algorithms discussed in Chapters4 and 5. It will be shown in Section4.2 that terminating the iterations prior to convergence is a means for regularizing the restoration process. Section4.3 presents a variation on the basic scheme which asymptotically produces the Tikhonov-Miller regularized solution. Finally, Section4.4 is concerned with procedures for increasing the convergence speed of the iterative algorithms.