Doicu / Trautmann / Schreier Numerical Regularization for Atmospheric Inverse Problems

1. Auflage 2010
ISBN: 978-3-642-05439-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 426 Seiten, eBook

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

Trautmann, Thomas

Schreier, Franz

Inhaltsverzeichnis

Chapter 1. Atmospheric remote sensingChapter 2. Ill-posedness of linear problemsChapter 3. Tikhonov regularization for linear problemsChapter 4. Statistical inversion theoryChapter 5. Iterative regularization methods for linear problemsChapter 6. Tikhonov regularization for nonlinear problemsChapter 7. Iterative regularization methods for nonlinear problemsChapter 8. Total least squaresChapter 9. Two direct regularization methodsAppendix A. Analysis of continuous ill-posed problemsAppendix B. A general direct regularization method for linear problemsAppendix C. A general iterative regularization method for linear problemsAppendix D. A general direct regularization method for nonlinear problemsAppendix E. A general iterative regularization method for nonlinear problems