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Very-High-Resolution and Interferometric SAR: Markovian and Patch-Based Non-local Mathematical Models

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Mathematical Models for Remote Sensing Image Processing

Part of the book series: Signals and Communication Technology ((SCT))

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Abstract

This chapter is dedicated to very-high-resolution (VHR) SAR imagery, including interferometric applications. First, the principles of SAR data acquisition are presented as well as the different types of configurations. The widely adopted Gaussian complex model of fully developed speckle is described as well as more advanced statistical models for VHR SAR data that account for textures. The following two parts are devoted to SAR image estimation and to image denoising within two different frameworks. First, Markovian modeling is introduced and the associated optimization approaches are presented, including graph-cut-based optimization. The second framework is the patch-based non-local modeling of SAR complex data. Both frameworks are adapted to SAR images through the use of statistical models specific to SAR imagery. Their applications to amplitude data, interferometry, and fusion with optical data are illustrated. A special focus is given to phase unwrapping applied to single- and multi-channel interferometry, showing the usefulness of local and global contextual models.

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Notes

  1. 1.

    The polarimetric case is mentioned in this chapter for completeness and to stress the generality of the described methods; it will be discussed more in-depth in the following chapter.

  2. 2.

    Corresponding to the backscattering coefficient \(\gamma (x,r)\) of the previous section but taking into account the amplitude factors.

  3. 3.

    \(\mathbb {E}\) is used here for the expectation operator, differently from the other chapters, for clarity and to avoid ambiguities.

  4. 4.

    In the following, we will denote by \({\mathbf {u}}\) the parameters of interest and \(\mathbf {v}\) the observations provided by the data in a generic way. If useful, these notations will be replaced by the notations introduced in Sect. 4.1.3 for SAR data.

  5. 5.

    Since each element of the random vector can be assigned to a given spatial location, we will refer to this random vector as a random field.

  6. 6.

    The vocabulary in use in Markov random fields theory comes from the field of statistical physics.

  7. 7.

    By global convergence, it is meant that the algorithm converges even if the initial value \({\mathbf {u}}^{(0)}\) is far from the optimum.

  8. 8.

    Also called an s-t-graph.

  9. 9.

    Note that edges connecting a node in \(\mathscr {T}\) to a node in \(\mathscr {S}\) do not enter the sum.

  10. 10.

    The maximum flow and the minimum cut problems can be formulated as two dual linear programs.

  11. 11.

    The class of MRF with cliques involving triplets is also covered in [52].

  12. 12.

    The method described in [57] applies to all convex pairwise terms \(\mathscr {R}\), see also [58, 59].

  13. 13.

    A total-variation regularization was applied on the optical image to remove low-significance textures.

  14. 14.

    In practice, they are empirically estimated using local samples and Eq. (4.35).

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Authors and Affiliations

  1. IMB, CNRS, University of Bordeaux, Bordeaux INP, 33405, Talence, France

    Charles-Alban Deledalle

  2. Univ Lyon, UJM-Saint-Etienne, CNRS, Institut d Optique Graduate School, Laboratoire Hubert Curien UMR 5516, F-42023, Saint-Etienne, France

    Loïc Denis

  3. Dipartimento di Scienze e Tecnologie, Università degli Studi di Napoli Parthenope, Centro Direzionale di Napoli, Is. C4, 80143, Naples, Italy

    Giampaolo Ferraioli

  4. Dipartimento di Ingegneria, Università degli Studi di Napoli Parthenope, Centro Direzionale di Napoli, Is. C4, 80143, Naples, Italy

    Vito Pascazio & Gilda Schirinzi

  5. LTCI, Telecom ParisTech, Université Paris Saclay, 46 rue Barrault, 75013, Paris, France

    Florence Tupin

Authors
  1. Charles-Alban Deledalle
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  2. Loïc Denis
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  3. Giampaolo Ferraioli
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  4. Vito Pascazio
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  5. Gilda Schirinzi
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  6. Florence Tupin
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Corresponding author

Correspondence to Florence Tupin .

Editor information

Editors and Affiliations

  1. University of Genoa, Genoa, Italy

    Gabriele Moser

  2. Université Côte d’Azur, Inria, Sophia Antipolis Cedex, France

    Josiane Zerubia

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Deledalle, CA., Denis, L., Ferraioli, G., Pascazio, V., Schirinzi, G., Tupin, F. (2018). Very-High-Resolution and Interferometric SAR: Markovian and Patch-Based Non-local Mathematical Models. In: Moser, G., Zerubia, J. (eds) Mathematical Models for Remote Sensing Image Processing. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-66330-2_4

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  • DOI: https://doi.org/10.1007/978-3-319-66330-2_4

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  • Print ISBN: 978-3-319-66328-9

  • Online ISBN: 978-3-319-66330-2

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