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Regularization of Ill-Posed Problems with Non-negative Solutions

In: Splitting Algorithms, Modern Operator Theory, and Applications

Author

Listed:
  • Christian Clason

    (University Duisburg-Essen, Faculty of Mathematics)

  • Barbara Kaltenbacher

    (Alpen-Adria Universität Klagenfurt, Institute of Mathematics)

  • Elena Resmerita

    (Alpen-Adria Universität Klagenfurt, Institute of Mathematics)

Abstract

This survey reviews variational and iterative methods for reconstructing non-negative solutions of ill-posed problems in infinite-dimensional spaces. We focus on two classes of methods: variational methods based on entropy-minimization or constraints, and iterative methods involving projections or non-negativity-preserving multiplicative updates. We summarize known results and point out some open problems.

Suggested Citation

  • Christian Clason & Barbara Kaltenbacher & Elena Resmerita, 2019. "Regularization of Ill-Posed Problems with Non-negative Solutions," Springer Books, in: Heinz H. Bauschke & Regina S. Burachik & D. Russell Luke (ed.), Splitting Algorithms, Modern Operator Theory, and Applications, chapter 0, pages 113-135, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-25939-6_5
    DOI: 10.1007/978-3-030-25939-6_5
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