An iterative method for linear discrete ill-posed problems with box constraints

Morigi, Serena; Reichel, Lothar; Sgallari, Fiorella; Zama, Fabiana

doi:10.1016/j.cam.2005.06.053

Cited by 20 publications

(29 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The method of this section is based on the iterative active set scheme described in [10] for finite dimensional problems. We therefore consider a discretization…”

Section: An Iterative Active Set Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Iterative Methods of Richardson-Lucy-Type for Image Deblurring

Khan¹

2013

NMTMA

View full text Add to dashboard Cite

Image deconvolution problems with a symmetric point-spread function arise in many areas of science and engineering. These problems often are solved by the Richardson-Lucy method, a nonlinear iterative method. We first show a convergence result for the Richardson-Lucy method. The proof sheds light on why the method may converge slowly Subsequently, we describe an iterative active set method that imposes the same constraints on the computed solution as the Richardson-Lucy method. Gomputed examples show the latter method to yield better restorations than the Richardson-Lucy method and typically require less computational effort.

show abstract

“…The method of this section is based on the iterative active set scheme described in [10] for finite dimensional problems. We therefore consider a discretization…”

Section: An Iterative Active Set Methodsmentioning

confidence: 99%

“…The iterative active set method in [10] is designed to determine an approximate solution of the constraint minimization problem where S c M'" is a convex set of feasible solutions defined by box constraints.…”

Section: L|ri^||<5 (33)mentioning

confidence: 99%

Iterative Methods of Richardson-Lucy-Type for Image Deblurring

Khan¹

2013

NMTMA

View full text Add to dashboard Cite

show abstract

“…Let y −1 ∈ R −1 denote the solution of the minimization problem analogous to (18) with replaced by − 1. BecauseC is lower bidiagonal, the vector made up of the first − 1 entries of y is a multiple of y −1 ; see, e.g., Björck [23, Section 7.6] or Paige and Saunders [24].…”

Section: Solution Of the Quadratic Modelmentioning

confidence: 99%

“…Large-scale linear discrete ill-posed problems with constraints arise in many applications and several different approaches to their solution have been proposed; see, e.g., Bardsley [13], Bertero and Boccacci [14, Section 6.3], Calvetti et al [15], Hanke et al [16], Kim [17], Morigi et al [18], Nagy and Strakoš [19], and references therein, in addition to the references already mentioned. There is presently not one best solution method for all constrained large-scale ill-posed problems.…”

Section: Introductionmentioning

confidence: 99%

An interior-point method for large constrained discrete ill-posed problems

Morigi

Reichel

Sgallari

2010

Journal of Computational and Applied Mathematics

Self Cite

View full text Add to dashboard Cite

a b s t r a c tIll-posed problems are numerically underdetermined. It is therefore often beneficial to impose known properties of the desired solution, such as nonnegativity, during the solution process. This paper proposes the use of an interior-point method in conjunction with truncated iteration for the solution of large-scale linear discrete ill-posed problems with box constraints. An estimate of the error in the data is assumed to be available. Numerical examples demonstrate the competitiveness of this approach.

show abstract

“…These methods have been shown to be an efficient tool to solve these problems even in the presence of degenerate solutions, see e.g. [2,18,20,21,24] In addition to active set approaches, Interior Point methods can be used to solve NNLS problems. They generate an infinite sequence of strictly feasible points converging to the solution and are known to be competitive with active set methods for medium and large problems.…”

mentioning

confidence: 99%