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2007, Volume 1, Issue 1: 29-46. Doi: 10.3934/ipi.2007.1.29
This issue Previous Article The interior transmission problem Next Article Integrodifferential equations for continuous multiscale wavelet shrinkage

Iteratively solving linear inverse problems under general convex constraints

  • 1.

    Princeton University, PACM, Washington Road, Princeton, NJ 08544-1000

  • 2.

    Konrad--Zuse--Institute Berlin, Takustr. 7, D-14195 Berlin-Dahlem

  • 3.

    Department of Mathematics, University of California, Los Angeles, 405 Hilgard Avenue, Los Angeles, CA 90095-1555

Received:  July 31, 2006
Revised:  August 31, 2006
Published:  January 2007
Abstract Related Papers Cited by
    Abstract
  • We consider linear inverse problems where the solution is assumed to fulfill some general homogeneous convex constraint. We develop an algorithm that amounts to a projected Landweber iteration and that provides and iterative approach to the solution of this inverse problem. For relatively moderate assumptions on the constraint we can always prove weak convergence of the iterative scheme. In certain cases, i.e. for special families of convex constraints, weak convergence implies norm convergence. The presented approach covers a wide range of problems, e.g. Besov-- or BV--restoration for which we present also numerical experiments in the context of image processing.
    Mathematics Subject Classification: Primary: 35, 41, 49; Secondary: 65.

    Citation:
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