An Algorithm for Splitting Parallel Sums of Linearly Composed Monotone Operators, with Applications to Signal Recovery - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Nonlinear and Convex Analysis Year : 2014

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

Stephen Becker
  • Function : Author
  • PersonId : 926707
Patrick Louis Combettes
  • Function : Author
  • PersonId : 940761

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.

Dates and versions

hal-00916084 , version 1 (09-12-2013)

Identifiers

Cite

Stephen Becker, Patrick Louis Combettes. An Algorithm for Splitting Parallel Sums of Linearly Composed Monotone Operators, with Applications to Signal Recovery. Journal of Nonlinear and Convex Analysis, 2014, 15 (1), pp.137-159. ⟨hal-00916084⟩
142 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More