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Mathematical and Statistical Methods for Multistatic Imaging

  • Book
  • © 2013

Overview

Authors:
  1. Habib Ammari

    1. Department of Mathematics and Applications, École Normale Supérieure, Paris, France

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  2. Josselin Garnier

    1. Laboratory of Probability and Random Mod, University Paris VII, Paris, France

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  3. Wenjia Jing

    1. Department of Mathematics and Applications, École Normale Supérieure, Paris, France

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  4. Hyeonbae Kang

    1. Department of Mathematics, Inha University, Incheon, Korea, Republic of (South Korea)

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  5. Mikyoung Lim

    1. Department of Mathematical Sciences, Korean Advanced Institute of Science and Technology (KASIT), Daejeon, Korea, Republic of (South Korea)

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  6. Knut Sølna

    1. Dept. Mathematics, University of California, Irvine School of Physical Sciences, Irvine, USA

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  7. Han Wang

    1. Department of Mathematics and Applications, École Normale Supérieure, Paris, France

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  • Fundamental contributions to multistatic imaging
  • New dictionary-matching techniques for imaging
  • Matlab codes for the main algorithms described in the book are provided
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2098)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xvii
    Download chapter PDF

  2. Mathematical and Probabilistic Tools

    1. Front Matter

      Pages 1-1
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    2. Preliminaries

      • Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 3-50

    3. Layer Potential Techniques

      • Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 51-94

  3. Small Volume Expansions and Concept of Generalized Polarization Tensors

    1. Front Matter

      Pages 95-95
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    2. Small Volume Expansions

      • Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 97-113

    3. Generalized Polarization Tensors

      • Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 115-131

    4. Frequency Dependent Generalized Polarization Tensors

      • Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 133-142

  4. Multistatic Configuration

    1. Front Matter

      Pages 143-143
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    2. Multistatic Response Matrix: Statistical Structure

      • Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 145-161

    3. MSR Matrices Using Multipolar Expansions

      • Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 163-169

  5. Localization and Detection Algorithms

    1. Front Matter

      Pages 171-171
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    2. Direct Imaging Functionals for Inclusions in the Continuum Approximation

      • Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 173-188

    3. Detection and Imaging from MSR Measurements

      • Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 189-202

  6. Dictionary Matching and Tracking Algorithms

    1. Front Matter

      Pages 203-203
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    2. Reconstruction of GPTs from MSR Measurements

      • Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 205-210

    3. Target Identification and Tracking

      • Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 211-226

  7. Imaging of Extended Targets

    1. Front Matter

      Pages 227-227
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    2. Time-Reversal and Diffraction Tomography for Inverse Source Problems

      • Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 229-238

    3. Imaging Small Shape Deformations of an Extended Target from MSR Measurements

      • Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 239-252
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Keywords

About this book

This book covers recent mathematical, numerical, and statistical approaches for multistatic imaging of targets with waves at single or multiple frequencies. The waves can be acoustic, elastic or electromagnetic. They are generated by point sources on a transmitter array and measured on a receiver array. An important problem in multistatic imaging is to quantify and understand the trade-offs between data size, computational complexity, signal-to-noise ratio, and resolution. Another fundamental problem is to have a shape representation well suited to solving target imaging problems from multistatic data.

In this book the trade-off between resolution and stability when the data are noisy is addressed. Efficient imaging algorithms are provided and their resolution and stability with respect to noise in the measurements analyzed. It also shows that high-order polarization tensors provide an accurate representation of the target. Moreover, a dictionary-matching technique based on new invariants for the generalized polarization tensors is introduced. Matlab codes for the main algorithms described in this book are provided. Numerical illustrations using these codes in order to highlight the performance and show the limitations of numerical approaches for multistatic imaging are presented.

Authors and Affiliations

  • Department of Mathematics and Applications, École Normale Supérieure, Paris, France

    Habib Ammari, Wenjia Jing, Han Wang

  • Laboratory of Probability and Random Mod, University Paris VII, Paris, France

    Josselin Garnier

  • Department of Mathematics, Inha University, Incheon, Korea, Republic of (South Korea)

    Hyeonbae Kang

  • Department of Mathematical Sciences, Korean Advanced Institute of Science and Technology (KASIT), Daejeon, Korea, Republic of (South Korea)

    Mikyoung Lim

  • Dept. Mathematics, University of California, Irvine School of Physical Sciences, Irvine, USA

    Knut Sølna

Bibliographic Information

  • Book Title: Mathematical and Statistical Methods for Multistatic Imaging

  • Authors: Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna, Han Wang

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-02585-8

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2013

  • Softcover ISBN: 978-3-319-02584-1Published: 17 December 2013

  • eBook ISBN: 978-3-319-02585-8Published: 29 November 2013

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVII, 361

  • Number of Illustrations: 14 b/w illustrations, 47 illustrations in colour

  • Topics: Mathematical Applications in the Physical Sciences

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