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Iteratively solving linear inverse problems under general convex constraints

Publication ,  Journal Article
Daubechies, I; Teschke, G; Vese, L
Published in: Inverse Problems and Imaging
January 1, 2007

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.

Duke Scholars

Published In

Inverse Problems and Imaging

DOI

EISSN

1930-8345

ISSN

1930-8337

Publication Date

January 1, 2007

Volume

1

Issue

1

Start / End Page

29 / 46

Related Subject Headings

  • 4904 Pure mathematics
  • 0103 Numerical and Computational Mathematics
  • 0101 Pure Mathematics
 

Citation

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Daubechies, I., Teschke, G., & Vese, L. (2007). Iteratively solving linear inverse problems under general convex constraints. Inverse Problems and Imaging, 1(1), 29–46. https://doi.org/10.3934/ipi.2007.1.29
Daubechies, I., G. Teschke, and L. Vese. “Iteratively solving linear inverse problems under general convex constraints.” Inverse Problems and Imaging 1, no. 1 (January 1, 2007): 29–46. https://doi.org/10.3934/ipi.2007.1.29.
Daubechies I, Teschke G, Vese L. Iteratively solving linear inverse problems under general convex constraints. Inverse Problems and Imaging. 2007 Jan 1;1(1):29–46.
Daubechies, I., et al. “Iteratively solving linear inverse problems under general convex constraints.” Inverse Problems and Imaging, vol. 1, no. 1, Jan. 2007, pp. 29–46. Scopus, doi:10.3934/ipi.2007.1.29.
Daubechies I, Teschke G, Vese L. Iteratively solving linear inverse problems under general convex constraints. Inverse Problems and Imaging. 2007 Jan 1;1(1):29–46.

Published In

Inverse Problems and Imaging

DOI

EISSN

1930-8345

ISSN

1930-8337

Publication Date

January 1, 2007

Volume

1

Issue

1

Start / End Page

29 / 46

Related Subject Headings

  • 4904 Pure mathematics
  • 0103 Numerical and Computational Mathematics
  • 0101 Pure Mathematics