A class of iterative signal restoration algorithms

Absfmct-In this paper, a class of iterative signal restoration algorithms i s derived 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 on-line and an offline computational part. The conditions for convergence, the rate of convergence of these algorithms, and the computational load required to achieve the same restoration result5 are derived. A new iterative algorithm i s 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 dimensionalitj. Iterative restoration algorithms that have appeared in the literature represent special cases of the class of algorithms described here. Therefore, the approach presented here unifies a large number of iterative restoration algorithms. Furthermore, ba\ed on the convergence properties of these algorithms, combined algorithms are proposed that incorporate apriori knowledge about the wlution in the form of constraints and converge faster than the previously used algorithms.