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.
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