A class of iterative signal restoration algorithms

Abstract
Absfmct-In this paper, a class of iterative signal restoration algo- rithms is derived based on a representation theorem for the general- ized inverse of a matrix. These algorithms exhibit a first or higher or- der of convergence, and some of them consist of an on-line and an off- line 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 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 dimensionalitj. Iterative restoration algorithms that have ap- peared in the literature represent special cases of the class of algo- rithms described here. Therefore, the approach presented here unifies a large number of iterative restoration algorithms. Furthermore, baed on the convergence properties of these algorithms, combined algo- rithms are proposed that incorporate apriori knowledge about the w- lution in the form of constraints and converge faster than the previ- ously used algorithms.

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