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Mathematical and Statistical Methods for Multistatic Imaging

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

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

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Mathematical and Probabilistic Tools

    1. Front Matter
      Pages 1-1
    2. Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 3-50
    3. 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
    2. Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 97-113
    3. Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 115-131
    4. 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
    2. Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 145-161
    3. 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
    2. Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 173-188
    3. 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
    2. Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 205-210
    3. 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
    2. Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 229-238
    3. Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 239-252
    4. Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 253-266
  8. Invisibility

    1. Front Matter
      Pages 267-267
    2. Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 269-286
    3. Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 287-299
  9. Numerical Implementations and Results

    1. Front Matter
      Pages 301-301
    2. Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 303-330
    3. Habib Ammari, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, Mikyoung Lim, Knut Sølna et al.
      Pages 331-349
  10. Back Matter
    Pages 351-382

About this book

Introduction

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.

Keywords

35R30,35B30 Detection, localization, and characterization Dictionary matching algorithms Mathematical imaging Optimal control algorithms Shape representations

Authors and affiliations

  • Habib Ammari
    • 1
  • Josselin Garnier
    • 2
  • Wenjia Jing
    • 3
  • Hyeonbae Kang
    • 4
  • Mikyoung Lim
    • 5
  • Knut Sølna
    • 6
  • Han Wang
    • 7
  1. 1.Department of Mathematics and ApplicationsÉcole Normale SupérieureParisFrance
  2. 2.Laboratory of Probability and Random ModUniversity Paris VIIParisFrance
  3. 3.Department of Mathematics and ApplicationsÉcole Normale SupérieureParisFrance
  4. 4.Department of MathematicsInha UniversityIncheonKorea, Republic of (South Korea)
  5. 5.Department of Mathematical SciencesKorean Advanced Institute of Science and Technology (KASIT)DaejeonKorea, Republic of (South Korea)
  6. 6.Dept. MathematicsUniversity of California, Irvine School of Physical SciencesIrvineUSA
  7. 7.Department of Mathematics and ApplicationsÉcole Normale SupérieureParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-02585-8
  • Copyright Information Springer International Publishing Switzerland 2013
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-02584-1
  • Online ISBN 978-3-319-02585-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site