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Large-Scale Inverse Problems in Imaging

  • Julianne Chung
  • Sarah Knepper
  • James G. Nagy
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Abstract

Large-scale inverse problems arise in a variety of significant applications in image processing, and efficient regularization methods are needed to compute meaningful solutions. This chapter surveys three common mathematical models including a linear model, a separable nonlinear model, and a general nonlinear model. Techniques for regularization and large-scale implementations are considered, with particular focus on algorithms and computations that can exploit structure in the problem. Examples from image deconvolution, multi-frame blind deconvolution, and tomosynthesis illustrate the potential of these algorithms. Much progress has been made in the field of large-scale inverse problems, but many challenges still remain for future research.

Keywords

Inverse Problem Singular Value Decomposition Regularization Parameter Point Spread Function Tikhonov Regularization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We would like to thank Eldad Haber, University of British Columbia, and Per Christian Hansen, Technical University of Denmark, for carefully reading the first draft of this chapter. Their comments and suggestions helped to greatly improve our presentation. The research of J. Chung is supported by the US National Science Foundation (NSF) under grant DMS-0902322. The research of J. Nagy is supported by the US National Science Foundation (NSF) under grant DMS-0811031, and by the US Air Force Office of Scientific Research (AFOSR) under grant FA9550-09-1-0487.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Virginia TechBlacksburg, VAUSA
  2. 2.Emory UniversityAtlanta, GAUSA
  3. 3.Emory UniversityAtlanta, GAUSA

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