  We present a new primal-dual splitting algorithm for structured monotone
inclusions in Hilbert spaces and analyze its asymptotic behavior. A novelty of
our framework, which is motivated by image recovery applications, is to
consider inclusions that combine a variety of monotonicity-preserving
operations such as sums, linear compositions, parallel sums, and a new notion
of parallel composition. The special case of minimization problems is studied
in detail, and applications to signal recovery are discussed. Numerical
simulations are provided to illustrate the implementation of the algorithm.
