Image Deblurring with Krylov Subspace Methods

Per Christian Hansen (Invited author)

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

    Abstract

    Image deblurring, i.e., reconstruction of a sharper image from a blurred and noisy one, involves the solution of a large and very ill-conditioned system of linear equations, and regularization is needed in order to compute a stable solution. Krylov subspace methods are often ideally suited for this task: their iterative nature is a natural way to handle such large-scale problems, and the underlying Krylov subspace provides a convenient mechanism to regularized the problem by projecting it onto a low-dimensional "signal subspace" adapted to the particular problem. In this talk we consider the three Krylov subspace methods CGLS, MINRES, and GMRES. We describe their regularizing properties, and we discuss some computational aspects such as preconditioning and stopping criteria.
    Original languageEnglish
    Title of host publicationProceedings of WSC 2011
    Publication date2011
    Publication statusPublished - 2011
    Event36th Conference of the Dutch-Flemish Numerical Analysis Communities: Woudschouten - Zeist, Netherlands
    Duration: 5 Oct 20117 Oct 2011
    Conference number: 36

    Conference

    Conference36th Conference of the Dutch-Flemish Numerical Analysis Communities
    Number36
    CountryNetherlands
    CityZeist
    Period05/10/201107/10/2011

    Cite this

    @inproceedings{6dd58ba42ad84b959868d5bb343471ed,
    title = "Image Deblurring with Krylov Subspace Methods",
    abstract = "Image deblurring, i.e., reconstruction of a sharper image from a blurred and noisy one, involves the solution of a large and very ill-conditioned system of linear equations, and regularization is needed in order to compute a stable solution. Krylov subspace methods are often ideally suited for this task: their iterative nature is a natural way to handle such large-scale problems, and the underlying Krylov subspace provides a convenient mechanism to regularized the problem by projecting it onto a low-dimensional {"}signal subspace{"} adapted to the particular problem. In this talk we consider the three Krylov subspace methods CGLS, MINRES, and GMRES. We describe their regularizing properties, and we discuss some computational aspects such as preconditioning and stopping criteria.",
    author = "Hansen, {Per Christian}",
    year = "2011",
    language = "English",
    booktitle = "Proceedings of WSC 2011",

    }

    Hansen, PC 2011, Image Deblurring with Krylov Subspace Methods. in Proceedings of WSC 2011. 36th Conference of the Dutch-Flemish Numerical Analysis Communities, Zeist, Netherlands, 05/10/2011.

    Image Deblurring with Krylov Subspace Methods. / Hansen, Per Christian (Invited author).

    Proceedings of WSC 2011. 2011.

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

    TY - GEN

    T1 - Image Deblurring with Krylov Subspace Methods

    AU - Hansen, Per Christian

    PY - 2011

    Y1 - 2011

    N2 - Image deblurring, i.e., reconstruction of a sharper image from a blurred and noisy one, involves the solution of a large and very ill-conditioned system of linear equations, and regularization is needed in order to compute a stable solution. Krylov subspace methods are often ideally suited for this task: their iterative nature is a natural way to handle such large-scale problems, and the underlying Krylov subspace provides a convenient mechanism to regularized the problem by projecting it onto a low-dimensional "signal subspace" adapted to the particular problem. In this talk we consider the three Krylov subspace methods CGLS, MINRES, and GMRES. We describe their regularizing properties, and we discuss some computational aspects such as preconditioning and stopping criteria.

    AB - Image deblurring, i.e., reconstruction of a sharper image from a blurred and noisy one, involves the solution of a large and very ill-conditioned system of linear equations, and regularization is needed in order to compute a stable solution. Krylov subspace methods are often ideally suited for this task: their iterative nature is a natural way to handle such large-scale problems, and the underlying Krylov subspace provides a convenient mechanism to regularized the problem by projecting it onto a low-dimensional "signal subspace" adapted to the particular problem. In this talk we consider the three Krylov subspace methods CGLS, MINRES, and GMRES. We describe their regularizing properties, and we discuss some computational aspects such as preconditioning and stopping criteria.

    M3 - Article in proceedings

    BT - Proceedings of WSC 2011

    ER -

    Hansen PC. Image Deblurring with Krylov Subspace Methods. In Proceedings of WSC 2011. 2011