-

 

 

 




Optimization Online





 

A VARIATIONAL FORMULATION FOR FRAME-BASED INVERSE PROBLEMS

C. Chaux(caroline.chaux***at***univ-mlv.fr)
P. L. Combettes(plc***at***math.jussieu.fr)
J.-C. Pesquet(pesquet***at***univ-mlv.fr)
V. R. Wajs(rozenbaum***at***ann.jussieu.fr)

Abstract: A convex variational framework is proposed for solving inverse problems in Hilbert spaces with a priori information on the representation of the target solution in a frame. The objective function to be minimized consists of a separable term penalizing each frame coefficient individually and of a smooth term modeling the data formation model as well as other constraints. Sparsity-constrained and Bayesian formulations are examined as special cases. A splitting algorithm is presented to solve this problem and its convergence is established in infinite-dimensional spaces under mild conditions on the penalization functions, which need not be differentiable. Numerical simulations demonstrate applications to frame-based image restoration.

Keywords: Convex programming, inverse problem, frame, Hilbert space

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Applications -- Science and Engineering (Other )

Citation: Technical report, Universite Paris 6, 75005 paris, France.

Download: [PDF]

Entry Submitted: 01/23/2007
Entry Accepted: 01/23/2007
Entry Last Modified: 01/23/2007

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society