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International Conference on Image Analysis and Recognition

ICIAR 2016: Image Analysis and Recognition pp 110–119Cite as

Image Denoising Using Euler-Lagrange Equations for Function-Valued Mappings

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9730))

Abstract

In this paper, we consider a new method for representing complex images, e.g., hyperspectral images and video sequences, in terms of function-valued mappings (FVMs), also known as Banach-valued functions. At each (pixel) location x, the FVM image u(x) is a function, as opposed to the traditional vector approach. We define the Fourier transform of an FVM as well as Euler-Lagrange conditions for functionals involving FVMs and then show how these results can be used to devise some FVM-based methods of denoising. We consider a very simple functional and present some numerical results.

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Acknowledgements

This research has been supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) in the form of a Discovery Grant (ERV). Financial support from the Faculty of Mathematics and the Department of Applied Mathematics (DO) is also gratefully acknowledged.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Daniel Otero, Davide La Torre & Edward R. Vrscay

  2. Department of Economics, Management, and Quantitative Methods, University of Milan, Milan, Italy

    Davide La Torre

  3. Department of Applied Mathematics and Sciences, Khalifa University, Abu Dhabi, UAE

    Davide La Torre

Authors
  1. Daniel Otero
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  2. Davide La Torre
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  3. Edward R. Vrscay
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Corresponding author

Correspondence to Edward R. Vrscay .

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Editors and Affiliations

  1. University of Porto, Porto, Portugal

    Aurélio Campilho

  2. Department of Electrical, University of Waterloo, Waterloo, Ontario, Canada

    Fakhri Karray

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Otero, D., La Torre, D., Vrscay, E.R. (2016). Image Denoising Using Euler-Lagrange Equations for Function-Valued Mappings. In: Campilho, A., Karray, F. (eds) Image Analysis and Recognition. ICIAR 2016. Lecture Notes in Computer Science(), vol 9730. Springer, Cham. https://doi.org/10.1007/978-3-319-41501-7_13

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  • DOI: https://doi.org/10.1007/978-3-319-41501-7_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-41500-0

  • Online ISBN: 978-3-319-41501-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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