Convergence of iterative signal reconstruction algorithms

This paper is concerned with the development of a general convergence proof which is applicable to a particular class of iterative signal reconstruction algorithms. The proof relies on the concept of a nonexpansive mapping and the uniqueness of the desired signal. Two specific iterative reconstruction algorithms which are considered to illustrate this method of proof are bandlimited extrapolation and phase-only signal reconstruction, the convergence proof of the later being a new result. The generality of the approach allows for the incorporation of nonlinear constraints such as positivity or minimum and maximum value constraints.