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We present a new primal-dual splitting algorithm for structured monotoneinclusions in Hilbert spaces and analyze its asymptotic behavior. A novelty ofour framework, which is motivated by image recovery applications, is toconsider inclusions that combine a variety of monotonicity-preservingoperations such as sums, linear compositions, parallel sums, and a new notionof parallel composition. The special case of minimization problems is studiedin detail, and applications to signal recovery are discussed. Numericalsimulations are provided to illustrate the implementation of the algorithm.

An Algorithm for Splitting Parallel Sums of Linearly Composed Monotone Operators, with Applications to Signal Recovery