Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems

Main definitions and notations
Introduction
Chapter 1. Finite-difference scheme inversion (FDSI)
1.1. Introduction
1.2. Volterra operator equations
1.3. Definitions and examples
1.4. Convergence of FDSI
1.5. Numerical examples
Chapter 2. Linearized multidimensional inverse problem
for the wave equation
2.1. Introduction
2.2. Problem formulation
2.3. Linearization
2.4. Analyzing the structure of the solution to one-dimensional direct
problem
2.5. Existence theorem for the direct problem
2.6. Uniqueness of solutions to the inverse problem and regularization
2.7. Numerical examples
vi Direct Methods of Solving Multidimensional Inverse Problems
Chapter 3. Methods of I.M. Gel'fand, B.M. Levitan
and M. G. Krein
3.1. Introduction
3.2. Gel'fand-Levitan-Krein (GLK) equation for one-dimensional
inverse problem
3.3. Multidimensional analog of GLK-equations
3.4. Gel'fand-Levitan method for wave equation
3.5. Discrete analog of the Gel'fand-Levitan equation
3.6. Multidimensional discrete analog
3.7. Numerical examples
Chapter 4. Boundary control method (BC method)
4.1. Introduction. Statement of the problem
4.2. BC method in one-dimensional case
4.3. BC method for 2D acoustic inverse problem
4.4. Numerical examples
Chapter 5. Projection method
5.1. Introduction
5.2. Projection method for solving inverse problem
for the wave equation
5.3. Projection method for solving inverse acoustic problem
5.4. Numerical examples
Appendix A
Appendix B
Bibliography