On Iterative Regularization and Its Application

Many existing techniques for image restoration can be expressed in terms of minimizing a particular cost function. Iterative regularization methods are a novel variation on this theme where the cost function is not fixed, but rather refined iteratively at each step. This provides an unprecedented degree of control over the tradeoff between the bias and variance of the image estimate, which can result in improved overall estimation error. This useful property, along with the provable convergence properties of the sequence of estimates produced by these iterative regularization methods lend themselves to a variety of useful applications. In this paper, we introduce a general set of iterative regularization methods, discuss some of their properties and applications, and include examples to illustrate them.