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Inverse Problems of Single Molecule Localization Microscopy

In: Time-dependent Problems in Imaging and Parameter Identification

Author

Listed:
  • Montse Lopez-Martinez

    (TU-Wien, Institute of Applied Physics)

  • Gwenael Mercier

    (University of Vienna, Faculty of Mathematics)

  • Kamran Sadiq

    (Johann Radon Institute for Computational and Applied Mathematics (RICAM))

  • Otmar Scherzer

    (University of Vienna, Faculty of Mathematics
    Johann Radon Institute for Computational and Applied Mathematics (RICAM))

  • Magdalena Schneider

    (TU-Wien, Institute of Applied Physics)

  • John C. Schotland

    (University of Michigan, Department of Mathematics and Department of Physics)

  • Gerhard J. Schütz

    (TU-Wien, Institute of Applied Physics)

  • Roger Telschow

    (University of Vienna, Faculty of Mathematics)

Abstract

Single molecule localization microscopy is a recently developed superresolution imaging technique to visualize structural properties of single cells. The basic principle consists in chemically attaching fluorescent dyes to the molecules, which after excitation with a strong laser may emit light. To achieve superresolution, signals of individual fluorophores are separated in time. In this paper we follow the physical and chemical literature and derive mathematical models describing the propagation of light emitted from dyes in single molecule localization microscopy experiments via Maxwell’s equations. This forms the basis of formulating inverse problems related to single molecule localization microscopy. We also show that the current status of reconstruction methods is a simplification of more general inverse problems for Maxwell’s equations as discussed here.

Suggested Citation

  • Montse Lopez-Martinez & Gwenael Mercier & Kamran Sadiq & Otmar Scherzer & Magdalena Schneider & John C. Schotland & Gerhard J. Schütz & Roger Telschow, 2021. "Inverse Problems of Single Molecule Localization Microscopy," Springer Books, in: Barbara Kaltenbacher & Thomas Schuster & Anne Wald (ed.), Time-dependent Problems in Imaging and Parameter Identification, pages 323-376, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-57784-1_12
    DOI: 10.1007/978-3-030-57784-1_12
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