-

 

 

 




Optimization Online





 

ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration

Daniela di Serafino (daniela.diserafino***at***unicampania.it)
Germana Landi (germana.landi***at***unibo.it)
Marco Viola (marco.viola***at***uniroma1.it)

Abstract: We propose a method, called ACQUIRE, for the solution of constrained optimization problems modeling the restoration of images corrupted by Poisson noise. The objective function is the sum of a generalized Kullback-Leibler divergence term and a TV regularizer, subject to nonnegativity and possibly other constraints, such as flux conservation. ACQUIRE is a line-search method that considers a smoothed version of TV, based on a Huber-like function, and computes the search directions by minimizing quadratic approximations of the problem, built by exploiting some second-order information. A classical second-order Taylor approximation is used for the Kullback-Leibler term and an iteratively reweighted norm approach for the smoothed TV term. We prove that the sequence generated by the method has a subsequence converging to a minimizer of the smoothed problem and any limit point is a minimizer. Furthermore, if the problem is strictly convex, the whole sequence is convergent. We note that convergence is achieved without requiring the exact minimization of the quadratic subproblems; low accuracy in this minimization can be used in practice, as shown by numerical results. Experiments on reference test problems show that our method is competitive with well-established methods for TV-based Poisson image restoration, in terms of both computational efficiency and image quality.

Keywords: Image restoration, Poisson noise, TV regularization, iteratively reweighted norm, quadratic approximation.

Category 1: Applications -- Science and Engineering (Other )

Category 2: Convex and Nonsmooth Optimization

Citation:

Download: [PDF]

Entry Submitted: 07/27/2018
Entry Accepted: 07/27/2018
Entry Last Modified: 08/21/2019

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 Optimization Society