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Regularization of Ill-Posed Problems with Non-negative Solutions

  • Christian ClasonEmail author
  • Barbara Kaltenbacher
  • Elena Resmerita
Chapter

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.

Keywords

Convex optimization Fenchel duality Entropy Regularization Sparsity Signal processing 

AMS 2010 Subject Classification

49M20 65K10 90C30 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Christian Clason
    • 1
    Email author
  • Barbara Kaltenbacher
    • 2
  • Elena Resmerita
    • 2
  1. 1.Faculty of MathematicsUniversity Duisburg-EssenEssenGermany
  2. 2.Institute of MathematicsAlpen-Adria Universität KlagenfurtKlagenfurtAustria

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