As the authors have written in the preface of the book the “principal goal for this book is to promote fundamental understanding of parameter estimation and inverse problem philosophy and methodology, specifically regarding such key issue as uncertainty, ill-posedness, regularization, bias and resolution”. Also, as the authors admit (see preface) “some advanced topics have been deliberately omitted from the book because of space limitations and/or because we expect that many raders would not be sufficiently familiar with the required mathematics”. In the omitted topics the following are included: “inverse scattering problems, seismic diffraction tomography, wavelets, data assimilation and expectation maximization methods”.
However, the authors have omitted in the text and in the references other important topics such as identification of coefficients and domains in partial differential equations and theoretical aspects concerning ill-posedness and conditioned stability. Such huge gap reduces the introductory character of the book and gives a mutilate view of what is the research in the field of inverse problems today.
Contents of the book: Ch. 1 Introduction, Ch. 2 Linear Regression, Ch. 3 Discretizing Continuous Inverse Problems, Ch. 4 Rank Deficiency and Ill-Conditioning, Ch. 5 Tikhonov Regularization, Ch. 6 Iterative Methods, Ch. 7 Additional Regularization Techniques, Ch. 8 Fourier Techniques, Ch. 9 Nonlinear Regression, Ch. 10 Nonlinear Inverse Problems, Ch. 11 Bayesian Methods, Appendix A Review of Linear Algebra, Appendix B Review of Probability and Statistics, Appendix C Review of Vector Calculus, Appendix D Glossary of Notation.