A unified approach to iterative signal restoration

Abstract

A class of iterative image restoration algorithms is derived. The algorithms are based on a representation theorem for the generalized inverse of a matrix. These algorithms exhibit a first or higher order of convergence and some of them consist of an online and an offline computation part. The conditions for convergence and the range of convergence of these algorithms are derived. An iterative algorithm is also presented which exhibits a higher rate of convergence than the standard quadratic algorithm with no extra computational load. These algorithms can be applied to the restoration of signals of any dimensionality. Iterative restoration algorithms that have appeared in the literature represent special cases of the class of algorithms described. Therefore, the approach presented unifies a large number of iterative restoration algorithms. >