Iterative restoration by generalized replacement

As an extension of the existing theory, iterative restoration algorithms are presented in this paper for the solution of noisy, nonlinear restoration problems. The constraints and distortions are assumed to be known and are modeled as general (not necessarily linear) projections. The constraints are divided into two fundamentally different types, system constraints and signal constraints, of which only the latter are susceptible to noise. These two types of constraints are imposed in separate steps, called the constraint and replacement steps, respectively. Comparison of the signals produced at each step enables one to determine whether or not the generated sequence of signals is converging. The problem caused by additive noise is overcome by modifying the replacement step. Such a modified replacement, called generalized replacement, improves both the quality of the reconstructed or restored signal and the convergence properties of the algorithm. The two types of generalized replacements considered in detail are partial replacement and windowed replacement.