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

Abstract

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.

Cited by in corpus (8)

• Perturbation estimation for the parallel sum of Hermitian positive semi-definite matrices
• Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems
• A new splitting method for solving composite monotone inclusions involving parallel-sum operators
• Convergence rate analysis of primal-dual splitting schemes
• Dual Smoothing and Level Set Techniques for Variational Matrix Decomposition
• Learning with Optimal Interpolation Norms
• Solving Coupled Composite Monotone Inclusions by Successive Fejér Approximations of Their Kuhn-Tucker Set
• A splitting algorithm for system of composite monotone inclusions