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## Introduction

*Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab*

### in Mathematical Methods in Elasticity Imaging

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691165318
- eISBN:
- 9781400866625
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691165318.003.0001
- Subject:
- Mathematics, Applied Mathematics

This book is about recent mathematical, numerical and statistical approaches for elasticity imaging of inclusions and cracks with waves at zero, single or multiple non-zero frequencies. It considers ... More

## Vibration Testing

*Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab*

### in Mathematical Methods in Elasticity Imaging

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691165318
- eISBN:
- 9781400866625
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691165318.003.0012
- Subject:
- Mathematics, Applied Mathematics

This chapter deals with vibration testing, which aims to identify inclusions, cracks, or shape changes in a structure by measuring its modal characteristics. The measured eigenparameters are related ... More

## Backpropagation and Multiple Signal Classification Imaging of Small Inclusions

*Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab*

### in Mathematical Methods in Elasticity Imaging

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691165318
- eISBN:
- 9781400866625
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691165318.003.0006
- Subject:
- Mathematics, Applied Mathematics

This chapter deals with direct imaging of small inclusions and cracks in the static regime, focusing on MUSIC- and migration-type algorithms for detecting the small defects. MUSIC, reverse-time ... More

## Small-Volume Expansions of the Displacement Fields

*Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab*

### in Mathematical Methods in Elasticity Imaging

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691165318
- eISBN:
- 9781400866625
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691165318.003.0004
- Subject:
- Mathematics, Applied Mathematics

This chapter deals with small-volume expansions of the displacement fields. It first introduces the notion of elastic moment tensor, a geometric quantity associated with a small-volume inclusion, ... More

## Topological Derivative Based Imaging of Small Inclusions in the Time-Harmonic Regime

*Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab*

### in Mathematical Methods in Elasticity Imaging

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691165318
- eISBN:
- 9781400866625
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691165318.003.0007
- Subject:
- Mathematics, Applied Mathematics

This chapter introduces a topological derivative (TD) based imaging framework for detecting small inclusions in the time-harmonic regime. Based on a weighted Helmholtz decomposition of the TD based ... More

## Optimal Control Imaging of Extended Inclusions

*Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab*

### in Mathematical Methods in Elasticity Imaging

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691165318
- eISBN:
- 9781400866625
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691165318.003.0010
- Subject:
- Mathematics, Applied Mathematics

This chapter describes the use of time-reversal imaging techniques for optimal control of extended inclusions. It first considers the problem of reconstructing shape deformations of an extended ... More

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