A finite parameterization and iterative algorithms for constrained minimum norm signal reconstruction

Abstract

Summary form only given. Signal reconstruction from a limited set of linear measurements of a signal and prior knowledge of signal characteristics expressed as convex constraint sets were treated. The problem was posed in Hilbert space as the determination of the minimum norm element in the intersection of convex constraint sets and a linear variety with finite codimension. A finite parameterization for the optimal solution was derived, and the optimal parameter vector was shown to satisfy a system of nonlinear equations in a finite-dimensional Euclidean space. Iterative algorithms for determining the parameters were obtained, and convergence was shown to be quadratic for many applications. The results were applied to example multidimensional reconstruction problems.<>