Generalized convex set theoretic image recovery

In set theoretic image recovery, the constraints which do not yield convex sets in the chosen Hilbert solution space cannot be enforced. In some cases, however, such constraints may yield convex sets in other Hilbert spaces. We introduce a generalized product space formalism, through which constraints that are convex in different Hilbert spaces can be combined. A nonconvex problem with several sets is reduced to a convex problem with two sets in the product space, where it is solved via an alternating projection method. Applications are discussed