Computational Methods for Linear Inverse Problems
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Computational Methods for Inverse Problems 反问题的计算方法 反问题是指从“外部”或可用的噪声数据中恢复出“内部”或“隐藏”的信息时出现的数学问题。反问题出现在许多技术和科学领域，如医学和地球物理成像、电磁散射和无损检测等。这些问题通常是不适定的。线性反问题的计算方法课程将主要介绍基于正则化技术的求解线性反问题的可靠的数值方法。 |
Prerequisites: Numerical Linear Algebra, Probability
Highlights: 教研结合型课程，探讨反问题计算方法
Instructor
Kui Du, Email: kuidu@xmu.edu.cn Office: B603 Math Building, Haiyun Campus
References
Computational Methods for Inverse Problems (CMIP), Curtis R. Vogel, SIAM, 2002
Discrete Inverse Problems: Insight and Algorithms (DIP), Per Christian Hansen, SIAM, 2010
An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems (DAUQ), Luis Tenorio, SIAM, 2017
Regularization of Inverse Problems, arXiv:2001.00617, 2020
Bayesian Scientific Computing, Daniela Calvetti and Erkki Somersalo, Springer, 2023
Introduction to Bayesian Scientific Computing: Ten Lectures on Subjective Computing, Daniela Calvetti and Erkki Somersalo, Springer, 2007
Contents
Chapter 1: Introduction
Chapter 2: Analytical tools
Chapter 3: Numerical optimization tools
Chapter 4: Statistical estimation theory
Chapter 5: Image deblurring
Chapter 6: Parameter identification
Chapter 7: Regularization parameter selection methods
Chapter 8: Total variation regularization
Chapter 9: Nonnegativity constraints
Other
Chebfun-numerical computing with functions by Trefethen's team
Regularization Tools Version 4.1 by Hansen
Computational Uncertainty Quantification for Inverse Problems, DTU Compute