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

Stephen Becker (1) , Patrick Louis Combettes (1)

1 LJLL - Laboratoire Jacques-Louis Lions

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.

Mots clés: duality; image recovery; infimal convolution; monotone operator; parallel composition; parallel sum; proximity operator; splitting algorithm

Domaines: Optimisation et contrôle [math.OC]

Stephen Becker, Patrick Louis Combettes. An Algorithm for Splitting Parallel Sums of Linearly Composed Monotone Operators, with Applications to Signal Recovery. 2013. ⟨hal-00825885⟩