  In convex optimization, duality theory can sometimes lead to simpler solution
methods than those resulting from direct primal analysis. In this paper, this
principle is applied to a class of composite variational problems arising in
particular in signal recovery. These problems are not easily amenable to
solution by current methods but they feature Fenchel-Moreau-Rockafellar dual
problems that can be solved by forward-backward splitting. The proposed
algorithm produces simultaneously a sequence converging weakly to a dual
solution, and a sequence converging strongly to the primal solution. Our
framework is shown to capture and extend several existing duality-based signal
recovery methods and to be applicable to a variety of new problems beyond their
scope.
