Compressed Sensing and Electron Microscopy

  • Peter Binev
  • Wolfgang Dahmen
  • Ronald DeVore
  • Philipp Lamby
  • Daniel Savu
  • Robert Sharpley
Chapter
Part of the Nanostructure Science and Technology book series (NST)

Abstract

Compressed sensing (CS) is a relatively new approach to signal acquisition which has as its goal to minimize the number of measurements needed of the signal in order to guarantee that it is captured to a prescribed accuracy. It is natural to inquire whether this new subject has a role to play in electron microscopy (EM). In this chapter, we shall describe the foundations of CS and then examine which parts of this new theory may be useful in EM.

Keywords

Zeolite Coherence Vanadate Molybdenum Expense 

Notes

Acknowledgments

We are very indebted to Doug Blom and Sonali Mitra for providing us with several STEM simulations, without which we would not have been able to validate the algorithmic concepts. Numerous discussions with Tom Vogt and Doug Blom have provided us with invaluable sources of information, without which this research would not have been possible. We are also very grateful to Nigel Browning for providing tomography data. We would also like to thank Andreas Platen for his assistance in preparing the numerical experiments.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Peter Binev
    • 1
  • Wolfgang Dahmen
    • 2
  • Ronald DeVore
    • 3
  • Philipp Lamby
    • 1
  • Daniel Savu
    • 1
  • Robert Sharpley
    • 1
  1. 1.Department of Mathematics and the Interdisciplinary Mathematics InstituteUniversity of South CarolinaColumbiaUSA
  2. 2.Institut für Geometrie und Praktische Mathematik, Department of MathematicsRWTH AachenAachenGermany
  3. 3.Department of MathematicsTexas A&M UniversityCollege StationUSA

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