A class of iterative signal restoration algorithms

Abstract

A class of iterative signal restoration algorithms is 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 online 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 results 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. The presented approach unifies a large number of iterative restoration algorithms. Based on the convergence properties of these algorithms, combined algorithms are proposed that incorporate a priori knowledge about the solution in the form of constraints and converge faster than previously published algorithms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>