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RFMP: An Iterative Best Basis Algorithm for Inverse Problems in the Geosciences

Abstract

We summarize a recently introduced greedy algorithm for inverse problems in geomathematics. The algorithm is able to combine heterogeneous systems of trial functions to construct a stable approximation to the solution of the given ill-posed problem. The representation of this approximation with respect to the trial functions of mixed types is sparse in the sense that essentially less trial functions than available are used. Some new theoretical results about the method are also proved here.

Keywords

  • Inverse Problem
  • Orthogonal Polynomial
  • Spherical Harmonic
  • Trial Function
  • Match Pursuit

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.

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Acknowledgements

The support by the German Research Foundation (project number DFG MI 655/7-1) is gratefully acknowledged. Moreover, the author wishes to thank Roger Telschow for proofreading the manuscript.

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Correspondence to Volker Michel .

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Michel, V. (2013). RFMP: An Iterative Best Basis Algorithm for Inverse Problems in the Geosciences. In: Freeden, W., Nashed, M., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27793-1_93-1

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  • DOI: https://doi.org/10.1007/978-3-642-27793-1_93-1

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