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Linear and nonlinear inverse problems with practical applications 1st Edition by Jennifer Mueller, Samuli Siltanen ISBN 1611972337 9781611972337

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Linear and nonlinear inverse problems with practical applications 2012.11.15 Edition Jennifer L. Mueller Digital Instant Download

Author(s): Jennifer L. Mueller , Samuli Siltanen
ISBN(s): 9781611972337, 1611972337
Edition: 2012.11.15
File Details: PDF, 42.59 MB
Year: 2012
Language: english
SKU: EB-42218546 Category: Tags: ,

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Product details:
ISBN 10: 1611972337
ISBN 13: 9781611972337
Author: Jennifer Mueller, Samuli Siltanen

Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book explains how to identify ill-posed inverse problems arising in practice and gives a hands-on guide to designing computational solution methods for them, with related codes on an accompanying website. The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer. A thorough treatment of electrical impedance tomography is used as the guiding nonlinear inversion example which combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner. This book is complete with exercises and project topics, making it ideal as a classroom textbook or self-study guide for graduate and advanced undergraduate students in mathematics, engineering or physics who wish to learn about computational inversion. It also acts as a useful guide for researchers who develop inversion techniques in high-tech industry.

Linear and nonlinear inverse problems with practical applications 1st Edition Table of contents:

Chapter 1: Introduction to Inverse Problems

  • Definition and Overview of Inverse Problems
  • Linear vs. Nonlinear Inverse Problems
  • General Problem Formulation and Mathematical Setup
  • Types of Inverse Problems and Their Applications

Chapter 2: Linear Inverse Problems

  • Overview of Linear Systems
  • Mathematical Formulation of Linear Inverse Problems
  • Direct and Iterative Solution Methods
  • Regularization Techniques for Ill-posed Problems
  • Case Studies and Applications in Image Reconstruction and Signal Processing

Chapter 3: Nonlinear Inverse Problems

  • Nonlinear Models and Their Challenges
  • Numerical Methods for Solving Nonlinear Inverse Problems
  • Convergence and Stability Issues in Nonlinear Problems
  • Regularization Techniques for Nonlinear Problems
  • Applications in Geophysics, Medical Imaging, and Optics

Chapter 4: Ill-posedness and Regularization

  • Understanding Ill-posed Problems
  • The Role of Regularization in Stabilizing Solutions
  • Tikhonov Regularization and Variants
  • Total Variation and Sparse Regularization
  • Choosing the Right Regularization Method for Different Applications

Chapter 5: Iterative Methods and Optimization

  • Overview of Iterative Methods for Solving Inverse Problems
  • Gradient-based and Non-gradient-based Optimization Methods
  • Conjugate Gradient Methods
  • Gauss-Newton and Levenberg-Marquardt Algorithms
  • Application to Practical Inverse Problems

Chapter 6: Statistical Methods for Inverse Problems

  • Bayesian Inference for Inverse Problems
  • Maximum Likelihood Estimation
  • Markov Chain Monte Carlo Methods
  • Uncertainty Quantification in Inverse Problems
  • Application of Statistical Methods in Medical Imaging

Chapter 7: Inverse Problems in Imaging and Signal Processing

  • Image Reconstruction Techniques
  • Tomography and Medical Imaging Applications
  • Inverse Problems in Signal Processing and Communication
  • Practical Examples from MRI, CT Scanning, and Radio Astronomy

Chapter 8: Nonlinear Inverse Problems in Geophysics and Earth Sciences

  • Inverse Problems in Seismology and Geophysical Imaging
  • Oceanography and Atmospheric Applications
  • Solution Methods for Large-scale Geophysical Problems

Chapter 9: Case Studies of Practical Applications

  • Industrial Applications of Inverse Problems
  • Inverse Problems in Environmental Science and Remote Sensing
  • Real-life Case Studies from Engineering and Medicine

Chapter 10: Advanced Topics and Future Directions

  • Emerging Techniques in Inverse Problems
  • Machine Learning Approaches to Inverse Problems
  • Hybrid Methods Combining Physics and Data-driven Models
  • The Future of Inverse Problems in Scientific Research

Conclusion

  • Summary of Key Concepts and Techniques
  • Challenges and Opportunities in Solving Inverse Problems

Appendix A: Mathematical Tools and Concepts

  • Overview of Key Mathematical Techniques Used in Inverse Problems
  • Linear Algebra and Optimization Theory Refresher

Appendix B: Software and Computational Tools

  • Overview of Tools and Libraries for Solving Inverse Problems
  • Practical Guide to Implementing Algorithms

References

  • Key References and Further Reading

Index

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