A finite parametrization for constrained minimum norm interpolants

Signal reconstruction from a limited set of linear measurements of a signal and prior knowledge of signal characteristics expressed as convex constraint sets is discussed. The problem is 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 parametrization for the optimal solution is derived, and the optimal parameter vector is shown to satisfy a system of nonlinear equations in a finite-dimensional Euclidean space. Iterative algorithms to determine the parameters are presented, and these results are applied to obtain a quadratically convergent algorithm solving a constrained power spectrum estimation problem