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Asymptotic expansions for the Helmholtz equation
Far- and near-field asymptotic formulas for the transient wave equation
Imaging in visco-elastic media obeying a frequency power-law
General visco-elastic wave equation
Table of contents :
Introduction
Introduction en Francais
Acknowledgments
Chapter 1. Transient acoustic imaging
1.1. Introduction 7
1.2. Asymptotic expansions for the Helmholtz equation
1.3. Far- and near-field asymptotic formulas for the transient wave equation
1.4. Reconstruction methods
1.5. Numerical illustrations
1.6. Concluding remarks
Chapter 2. Transient elasticity imaging and time reversal
2.1. Introduction
2.2. Asymptotic expansions
2.3. Far- and near-field asymptotic formulas in the transient regime
2.4. Asymptotic imaging
2.5. Concluding remarks
Chapter 3. Transient imaging with limited-view data
3.1. Introduction
3.2. Geometric control
3.3. Imaging algorithms
3.4. Applications to emerging biomedical imaging
3.5. Numerical illustrations
3.6. Concluding remarks
Chapter 4. Imaging in visco-elastic media obeying a frequency power-law
4.1. Introduction
4.2. General visco-elastic wave equation
4.3. Green’s function
4.4. Imaging procedure
4.5. Numerical illustrations
4.6. Concluding remarks
Appendix A: Proof of the approximation formula
Bibliography
