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Total Variation Minimization for Measure-Valued Images with Diffusion Spectrum Imaging as Motivation

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Abstract

In this paper, we present a notion of total variation for measure-valued images. Our motivation is Diffusion Spectrum Imaging (DSI) in which the diffusion at each voxel is characterized by a probability density function. We introduce a total variation denoising problem for measure-valued images. In the one-dimensional case, this problem (which involves the Monge-Kantorovich metric for measures) can be solved using cumulative distribution functions. In higher dimensions, more computationally expensive methods must be employed.

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Acknowledgements

This work has also been supported in part by Discovery Grants from the Natural Sciences and Engineering Research Council of Canada (NSERC): FM (238549-2012) and ERV (Grant No. 106270-2012).

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Authors and Affiliations

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

    Davide La Torre

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

    Davide La Torre

  3. Department of Mathematics and Statistics, Acadia University, Wolfville, NS, Canada

    Franklin Mendivil

  4. Deparment of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada

    Oleg Michailovich

  5. Deparment of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada

    Edward R. Vrscay

Authors
  1. Davide La Torre
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  2. Franklin Mendivil
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  3. Oleg Michailovich
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  4. Edward R. Vrscay
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Corresponding author

Correspondence to Edward R. Vrscay .

Editor information

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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La Torre, D., Mendivil, F., Michailovich, O., Vrscay, E.R. (2016). Total Variation Minimization for Measure-Valued Images with Diffusion Spectrum Imaging as Motivation. 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_15

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  • DOI: https://doi.org/10.1007/978-3-319-41501-7_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-41500-0

  • Online ISBN: 978-3-319-41501-7

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