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Deconvolution and Denoising for Confocal Microscopy

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Modeling in Computational Biology and Biomedicine

Abstract

Fluorescence light microscopes, especially the confocal laser scanning microscopes, have become a powerful tool in life sciences for observing biological samples in order to detect the distribution of proteins or other molecules of interest. Using this tool, biologists can study cells and their sub-cellular structures, identify, and precisely localize cellular organelles and supra-molecular structures. The confocal microscope is a type of fluorescent light microscope that gives very good two-dimensional optical sections of three-dimensional specimens, rejects the background auto-fluorescence, and offers a good contrast. However, there are some inherent limitations in confocal images such as the blurring effects due to the diffraction limit of the optics, and the low signal levels. The aim of this chapter is to introduce the reader to the basics of the light and confocal microscopes, their imaging limitations, and the mathematics involved in the resolution and signal-to-noise ratio improvement methodologies. Although user-friendly restoration software packages are available in the market, image restoration by deconvolution remains a difficult task for many microscopist and choosing the right software is often a case of trial and error due to a lack of knowledge of the applied algorithm. It is with the objective of resolving this issue that the most recent developments are intuitively explained, with some concrete examples to explain the underlying principles. The current open problems in the field of microscopy and methodological challenges are mentioned towards the end of the chapter.

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Notes

  1. 1.

    The near field (or near-field), far field (or far-field), and the transition zone are regions of the electromagnetic radiation field scattering off an object. Certain characteristics of electromagnetic fields dominate at a large distance (or zone) from the scattering object, while a different characteristic can dominate at a shorter distance.

  2. 2.

    Molecules having two states, one fluorescent and the other non-fluorescent, and the ability to be switched from one state to the other by excitation with a shortwave light.

  3. 3.

    The numerical aperture of a lens measures its maximum light collection angle. It can be calculated as \(\mathrm{NA} = n\sin \alpha \), where n is the refractive index of the imaging medium between the objective lens and the coverglass, and α is the maximum semi-angle subtended by the incident light cone accepted by the lens.

  4. 4.

    Back-projected diameter is the diameter of a pinhole in the object space. It is equal to the ratio between the real physical diameter of the pinhole and the total magnification of the system.

  5. 5.

    Quantum efficiency for a photosensitive device measures the percentage of photons hitting the photoreactive surface that will produce an electron-hole pair. It is an accurate measurement of the device’s electrical sensitivity to light.

  6. 6.

    The quantum yield of a radiation-induced process is the number of times that a photon is emitted per photon absorbed by the system. This is essentially the emission efficiency of a given fluorophore.

  7. 7.

    A given problem is said to be ill-conditioned when it has a high condition number or the solution changes by a very significant amount in proportion to very small changes in the input data.

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Acknowledgements

Part of the results presented in this chapter was funded by the P2R Franco-Israeli collaborative research program and the ANR DIAMOND project. The authors gratefully acknowledge Prof. Zvi Kam (Weizmann Institute of Sciences, Israel) and Dr. Jean-Christophe Olivo-Marin (Institut Pasteur, Paris, France) for several interesting discussions. Additionally, our sincere gratitude goes to the editors, and Prof. James B. Pawley (Department of Zoology, University of Wisconsin, Madison, USA) Dr. Francois Orieux (Paris Institute of Astrophysics, France) for their detailed reviews and suggestions.

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Authors and Affiliations

  1. Institut Pasteur, 25 rue du Docteur Roux, 75724, Paris, France

    Praveen Pankajakshan

  2. INRA, 400 route des Chappes, 06903, Sophia Antipolis, France

    Gilbert Engler

  3. I3S (CNRS/UNS) UMR 7271 CNRS/UNSA and Inria, Algorithmes/Euclide-B, 2000 Route des Lucioles, 06903, Sophia Antipolis, France

    Laure Blanc-Féraud

  4. Inria Sophia Antipolis Méditerranée, Ariana project-team, 2004 Route des Lucioles, 06902, Sophia Antipolis, France

    Josiane Zerubia

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  1. Praveen Pankajakshan
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  1. , Algorithms-Biology-Structure, INRIA Sophia Antipolis - Méditerranée, Route des Lucioles 2004, Sophia Antipolis, 06902, France

    Frédéric Cazals

  2. , NeuroMathComp project team, INRIA Sophia Antipolis - Méditerranée, Route des Lucioles 2004, Sophia Antipolis, 06902, France

    Pierre Kornprobst

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Pankajakshan, P., Engler, G., Blanc-Féraud, L., Zerubia, J. (2013). Deconvolution and Denoising for Confocal Microscopy. In: Cazals, F., Kornprobst, P. (eds) Modeling in Computational Biology and Biomedicine. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31208-3_4

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