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Two direct regularization methods

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Numerical Regularization for Atmospheric Inverse Problems

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Abstract

In this chapter we present two direct regularization methods, namely the Backus-Gilbert method and the maximum entropy regularization. Although these approaches have been designed for linear problems they can be applied to nonlinear problems as well.

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References

  • Backus, G. and Gilbert, F. (1967). Numerical applications of a formalism for geophysical inverse problems. Geophys. J. R. Astron. Soc. 13, 247—276.

    Google Scholar 

  • Eggermont, P. P. B. (1993). Maximum entropy regularization for Fredholm integral equations of the first kind. SIAM J. Math. Anal. 24, 1557—1576.

    Article  Google Scholar 

  • Engl, H. W., Hanke, M., and Neubauer, A. (2000). Regularization of Inverse Problems. Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Frieden, B. R. (1972). Restoring with maximum likelihood and maximum entropy. J. Opt. Soc. Am. 62, 511—518.

    Article  CAS  Google Scholar 

  • Jaynes, E. T. (1957). Information theory and statistical mechanics. Phys. Rev. 106, 620—630.

    Article  Google Scholar 

  • Louis, A. K. and Maass, P. (1990). A mollifier method for linear operator equations of the first kind. Inverse Problems 6, 427—440.

    Article  Google Scholar 

  • Ramos, F. M., Velho, H. F. C., Carvalho, J. C., and Ferreira, N. J. (1999). Novel approaches to entropic regularization. Inverse Problems 15, 1139—1148.

    Article  Google Scholar 

  • Rieder, A. and Schuster, T. (2000). The approximate inverse in action with an application to computerized tomography. SIAM J. Numer. Anal. 37, 1909—9120.

    Article  Google Scholar 

  • Shannon, C. E. (1949). Communication in the presence of noise. Proc. ICE 37, 10—21

    Google Scholar 

  • Shannon, C. E. and Weaver, W. (1949). The Mathematical Theory of Communication. Uni-versity of Illinois Press, Urbana, IL.

    Google Scholar 

  • Steinwagner, J., Schwarz, G., and Hilgers, S. (2006). Use of maximum entropy method as a regularization technique during the retrieval of trace gas profiles from limb sounding measurements. J. Atmos. Oceanic Tech. 23, 1657—1667.

    Article  Google Scholar 

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Doicu, A., Trautmann, T., Schreier, F. (2010). Two direct regularization methods. In: Numerical Regularization for Atmospheric Inverse Problems. Springer Praxis Books(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05439-6_9

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