A PROJECTION-BASED ALGORITHM FOR CONSISTENT AND INCONSISTENT CONSTRAINTS

Signal synthesis and reconstruction is considered when the signal is t o be determined by N constraint sets, C-i. The solution sought is requ ired to minimize a weighted quadratic cost functional (J) over cap. Em phasis is on cases in which the intersection of the sets C-i is empty. Our proposed procedure employs a suitably weighted simultaneous proje ction iteration method. It is shown that the iterates generated by the algorithm converge weakly to a global minimizer of (J) over cap provi ded the set of fixed points of the algorithm is nonempty. If the probl em is consistent (C-o := boolean AND C-i not equal phi), weak converge nce is to an element in C-o. However, it is indicated that large class es of inconsistent problems, which could not be treated by existing me thods, admit a solution as well.