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Compressed Sensing and Electron Microscopy

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Modeling Nanoscale Imaging in Electron Microscopy

Part of the book series: Nanostructure Science and Technology ((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.

This research was supported in part by the College of Arts and Sciences at the University of South Carolina; the ARO/DoD Contracts W911NF-05-1-0227 and W911NF-07-1-0185; the Office of Naval Research Contract ONR-N00014-08-1-1113; the NSF Grants DMS-0915104 and DMS-0915231; the Special Priority Program SPP 1324, funded by German Research Foundation; and National Academies Keck Futures Initiative grant NAKFI IS11.

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Notes

  1. 1.

    In mathematics, the symbol “ : = ” is used to mean that the quantity nearest the colon “:” is defined by the quantity nearest the equal sign “=”.

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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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Authors and Affiliations

  1. Department of Mathematics and the Interdisciplinary Mathematics Institute, University of South Carolina, Columbia, SC, 29208, USA

    Peter Binev, Philipp Lamby, Daniel Savu & Robert Sharpley

  2. Institut für Geometrie und Praktische Mathematik, Department of Mathematics, RWTH Aachen, 52056, Aachen, Germany

    Wolfgang Dahmen

  3. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA

    Ronald DeVore

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  1. Peter Binev
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  2. Wolfgang Dahmen
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  3. Ronald DeVore
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  4. Philipp Lamby
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  5. Daniel Savu
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  6. Robert Sharpley
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Corresponding author

Correspondence to Peter Binev .

Editor information

Editors and Affiliations

  1. NanoCenter, Dept. of Chemistry & Biochem., University of South Carolina, Greene Street 1212, Columbia, 29208, South Carolina, USA

    Thomas Vogt

  2. , Dept. of Mathematics, Inst. Geometrie & Praktische Mathemat., Templergraben 55, Aachen, 52056, Germany

    Wolfgang Dahmen

  3. Interdisciplin. Mathematics Instit., Dept. Mathematics, University of South Carolina, Greene Street 1523, Columbia, 29208, South Carolina, USA

    Peter Binev

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Binev, P., Dahmen, W., DeVore, R., Lamby, P., Savu, D., Sharpley, R. (2012). Compressed Sensing and Electron Microscopy. In: Vogt, T., Dahmen, W., Binev, P. (eds) Modeling Nanoscale Imaging in Electron Microscopy. Nanostructure Science and Technology. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-2191-7_4

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