Fischer, Doreen: Sparse regularization of a joint inversion of gravitational data and normal mode anomaliesKombinierte Inversion von Gravitationsdaten und Normal-Mode-Anomalien mittels Sparse Regularization. 2011
Content
- Acknowledgements
- Abstract
- Zusammenfassung
- Contents
- Introduction
- I. Fundamentals
- 1. Preliminaries
- 1.1. Basic Settings and Spherical Geometry
- 1.2. Orthogonal Polynomials
- 1.3. Kernel Functions
- 1.4. Inverse Problems
- 1.5. Foundations of Functional Analysis
- 1.6. Sobolev Spaces
- 1.7. Point Grids
- 2. Basic Problems
- II. Matching Pursuit
- 3. Functional Matching Pursuit
- 3.1. Sparse Regularization and Overcomplete Signal Representation
- 3.2. The Algorithm
- 3.3. Theoretical Results
- 3.4. Outlook: Orthogonal Matching Pursuit
- 3.5. Implementation of the Basic Functional Matching Pursuit
- 4. Regularized Functional Matching Pursuit
- 4.1. The Algorithm
- 4.2. Theoretical Results
- 4.3. Implementation of the Regularized Basic Functional Matching Pursuit
- 4.4. Alternative: The Least Mixed Norms Problem (MRFMP)
- III. Numerical Applications
- 5. Reconstructing the Mass Density Distribution of the Earth
- 5.1. by Using Gravimetric Data (EGM2008): Example South America
- 5.2. Remark: The Sparse Regularization Point of View (MRFMP _l1)
- 5.3. by Combining Gravitational and Normal Mode Data
- 6. Reconstructing the Mass Transport in the Amazon Area
- IV. In the End
- 7. Summary
- 8. Outlook
- V. Appendix
- Bibliography
- Index