Parameter Estimation and Inverse Problems

Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do not have an extensive mathematical background. The book is complemented by a companion website that includes MATLAB codes that correspond to examples that are illustrated with simple, easy to follow problems that illuminate the details of particular numerical methods. Updates to the new edition include more discussions of Laplacian smoothing, an expansion of basis function exercises, the addition of stochastic descent, an improved presentation of Fourier methods and exercises, and more.

• Features examples that are illustrated with simple, easy to follow problems that illuminate the details of a particular numerical method
• Includes an online instructor’s guide that helps professors teach and customize exercises and select homework problems
• Covers updated information on adjoint methods that are presented in an accessible manner

Graduate and advanced undergraduate students taking courses in geophysical inverse problems. It is also used as a reference for geoscientists and researchers in academe and industry

1. Introduction
2. Linear Regression
3. Rank Deficiency and Ill-Conditioning
4. Tikhonov Regularization
5. Discretizing by Basis Functions
6. Iterative Methods of Solving Linear Problems
7. Additional Regularization Techniques
8. Fourier Techniques
9. Nonlinear Regression
10. Nonlinear Inverse Problems
11. Bayesian Methods
12 Adjoint Methods