Numerical Regularization for Atmospheric Inverse Problems

2010
ISBN: 978-3-642-42401-4
Verlag: Springer

Buch, Englisch, 426 Seiten, Paperback, Format (B × H): 168 mm x 240 mm, Gewicht: 733 g

Reihe: Springer Praxis Books

The retrieval problems arising in atmospheric remote sensing belong to the class of the - called discrete ill-posed problems. These problems are unstable under data perturbations, and can be solved by numerical regularization methods, in which the solution is stabilized by taking additional information into account. The goal of this research monograph is to present and analyze numerical algorithms for atmospheric retrieval. The book is aimed at physicists and engineers with some ba- ground in numerical linear algebra and matrix computations. Although there are many practical details in this book, for a robust and ef?cient implementation of all numerical algorithms, the reader should consult the literature cited. The data model adopted in our analysis is semi-stochastic. From a practical point of view, there are no signi?cant differences between a semi-stochastic and a determin- tic framework; the differences are relevant from a theoretical point of view, e.g., in the convergence and convergence rates analysis. After an introductory chapter providing the state of the art in passive atmospheric remote sensing, Chapter 2 introduces the concept of ill-posedness for linear discrete eq- tions. To illustrate the dif?culties associated with the solution of discrete ill-posed pr- lems, we consider the temperature retrieval by nadir sounding and analyze the solvability of the discrete equation by using the singular value decomposition of the forward model matrix.

Zielgruppe

Research

Autoren/Hrsg.

Doicu, Adrian

Schreier, Franz

Trautmann, Thomas

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Geowissenschaften Geographie | Raumplanung Geodäsie, Kartographie, GIS, Fernerkundung
• Geowissenschaften Geologie Geodäsie, Kartographie, Fernerkundung
• Geowissenschaften Geologie Meteorologie, Klimatologie

Inhaltsverzeichnis

Chapter 1. Atmospheric remote sensing

Chapter 2. Ill-posedness of linear problems

Chapter 3. Tikhonov regularization for linear problems

Chapter 4. Statistical inversion theory

Chapter 5. Iterative regularization methods for linear problems

Chapter 6. Tikhonov regularization for nonlinear problems

Chapter 7. Iterative regularization methods for nonlinear problems

Chapter 8. Total least squares

Chapter 9. Two direct regularization methods

Appendix A. Analysis of continuous ill-posed problems

Appendix B. A general direct regularization method for linear problems

Appendix C. A general iterative regularization method for linear problems

Appendix D. A general direct regularization method for nonlinear problems

Appendix E. A general iterative regularization method for nonlinear problems