INCONSISTENT SIGNAL FEASIBILITY PROBLEMS - LEAST-SQUARES SOLUTIONS INA PRODUCT SPACE

In this paper, we present parallel projection methods to find least-sq uares solutions to inconsistent convex set theoretic signal synthesis problems. The problem of finding a signal that minimizes a weighted av erage of the squares of the distances to constraint sets is reformulat ed in a product space, where it is equivalent to that of finding a poi nt that lies in a particular subspace and at minimum distance from the Cartesian product of the original sets. A solution is obtained in the product space via methods of alternating projections which naturally lead to methods of parallel projections in the original space. The con vergence properties of the proposed methods are analyzed and signal sy nthesis applications are demonstrated.