A Class of Iterative Signal Restoration Algorithms

In this paper, a class of iterative signal restoration algorithms is derived based on a representation theorem for the general-zed 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 onditions for convergence, the rate ofconvergence of these algorithms, and the computational load required to achieve the same restoration results are erived. A new iterative algorithm is also presented which exhibits a higher rate of convergence than the standard quadratic algorithm with no extra omputational load. These algorithms can be applied to the restoration of signals of any dimensionality. Iterative restoration algorithms that have appeared in he literature represent special cases of the class of algorithms described here. Therefore, the approach presented here unifies a large number of iterative estoration algorithms. Furthermore, based on the convergence properties of these algorithms, combined algorithms are proposed that incorporate a priori now ledge about the solution in the form of constraints and converge faster than the previously used algorithms.