Convergence of Iterative Nonexpansive Signal Reconstruction Algorithms

摘要

A convergence proof of a special class of iterative signal reconstruction problems is presented. The proof relies on the concept of nonexpansive mappings which impose partial knowledge of the unknown signal in both the time and frequency domains. Two examples studied in detail are time limited extrapolation and phase-only reconstruction. The proof of convergence for the phase-only iteration is a new result. The generality of the approach allows the incorporation of nonlinear constraints such as positivity or minimum and maximum values. Finally, the under-relaxed form of these iterations is shown to converge when the solution is not necessarily unique. (Author)