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Convergence Rates

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Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization

Part of the book series: Frontiers in Mathematics ((FM))

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Abstract

We derive asymptotic error estimates for the ℓ 1-distance between exact and ℓ 1-regularized solutions to linear operator equations. These estimates are based on variational source conditions.

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References

  1. R.E. Megginson, An Introduction to Banach Space Theory, Graduate Texts in Mathematics, vol. 183 (Springer, New York, 1998)

    Book  Google Scholar 

  2. M. Grasmair, M. Haltmeier, O. Scherzer, Communications on Pure and Applied Mathematics 64, 161 (2011)

    Article  MathSciNet  Google Scholar 

  3. M. Burger, J. Flemming, B. Hofmann, Inverse Problems 29, 025013 (16pp) (2013)

    Google Scholar 

  4. J. Flemming, D. Gerth, (2017). Submitted to Journal of Inverse and Ill-Posed Problems

    Google Scholar 

  5. M. Burger, S. Osher, Inverse Problems 20(5), 1411 (2004)

    Article  MathSciNet  Google Scholar 

  6. I. Daubechies, M. Defrise, C. De Mol, Communications on Pure and Applied Mathematics 57(11), 1413 (2004)

    Article  MathSciNet  Google Scholar 

  7. J. Flemming, M. Hegland, Applicable Analysis 94, 464 (2015)

    Article  MathSciNet  Google Scholar 

  8. J. Flemming, B. Hofmann, I. Veselić, Journal of Inverse and Ill-Posed Problems 24, 139 (2016)

    Article  MathSciNet  Google Scholar 

  9. J. Flemming, Inverse Problems 32(9), 095001 (19pp) (2016)

    Google Scholar 

  10. K. Bredies, D.A. Lorenz, Inverse Problems 25(8), 085011 (14pp) (2009)

    Google Scholar 

  11. M. Grasmair, Journal of Mathematical Analysis and Applications 365(1), 19 (2010)

    Article  MathSciNet  Google Scholar 

  12. D.A. Lorenz, Journal of Inverse and Ill-Posed Problems 16, 463 (2008)

    Article  MathSciNet  Google Scholar 

  13. M. Grasmair, Inverse Problems and Imaging 33, 383 (2009)

    Article  MathSciNet  Google Scholar 

  14. M. Grasmair, M. Haltmeier, O. Scherzer, Inverse Problems 24, 055020 (13pp) (2008)

    Google Scholar 

  15. T. Ramlau, E. Resmerita, Electronic Transactions on Numerical Analysis 37, 87 (2010)

    MathSciNet  Google Scholar 

  16. B. Hofmann, Mathematical Methods in the Applied Sciences 29(3), 351 (2006)

    Article  MathSciNet  Google Scholar 

  17. T. Hein, B. Hofmann, Inverse Problems 25(3), 035033 (16pp) (2009)

    Google Scholar 

  18. M. Grasmair, Well-posedness and convergence rates for sparse regularization with sublinear ℓ q penalty term. Industrial Geometry report 74, University of Innsbruck, Innsbruck, Austria (2008)

    Google Scholar 

  19. S.W. Anzengruber, B. Hofmann, R. Ramlau, Inverse Problems 29, 125002 (21pp) (2013)

    Google Scholar 

  20. K. Bredies, D.A. Lorenz, Journal of Fourier Analysis and Applications 14(5–6), 813 (2008)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Fakultät für Mathematik, Technische Universität Chemnitz, Chemnitz, Germany

    Jens Flemming

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  1. Jens Flemming
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Flemming, J. (2018). Convergence Rates. In: Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization. Frontiers in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-95264-2_11

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