Iterative Image Restoration

This chapter describes the class of iterative algorithms to the problem of restoring a noisy and blurred image. Iterative algorithms form an important part of optimization theory and numerical analysis. The basic idea behind such an algorithm is that the solution to the problem of recovering a signal, which satisfies certain constraints from its degraded observation, can be found by the alternate implementation of the degradation and the constraint operator. Problems that can be solved with such an iterative algorithm are the phase-only recovery problem, the magnitude-only recovery problem, the band-limited extrapolation problem, the image restoration problem, and the filter design problem. There are a number of advantages associated with iterative restoration algorithms, among which: there is no need to determine or implement the inverse of an operator, knowledge about the solution can be incorporated into the restoration process in a relatively straightforward manner, the solution process can be monitored as it progresses, and the partially restored signal can be utilized in determining unknown parameters pertaining to the solution.