Constrained parallel projection methods for optimal signal estimation and design-constrained inconsistent signal feasibility problems

The convex set feasibility framework has been widely applied to signal and image processing problems including signal deconvolution, tomographic reconstruction, band limited extrapolation, image restoration and image synthesis. In this paper, we consider convex constrained versions of inconsistent signal feasibility problems. First we derive some new properties of variational nonexpansive operators and convex projections. Based on these properties and fixed point theorems, we propose some types of algorithms called constrained parallel projection methods (CPPM) that solve the convex constrained versions of inconsistent signal feasibility problems