【注1】虽然咱不看这方面的内容，但是既然莫名其妙地下了这么个东西，就想着不能扔了，至少留一份于***当中。
【注2】简单排版，但并未校正，无法保证质量。
【注3】与原文不同，这里按照Mx做了重排，排法类似于大名鼎鼎的冒泡排序，故而more不保证质量。
A Reading List in Inverse Problems
Brian Borchers
Draft of January 13, 1998
摘要：本文档是与逆问题相关的各种主题的书籍、调查文章和在线文档的参考书目。 我尽量避免列出研究论文，因为关于这些主题的研究论文比我希望包含在本参考书目中的要多得多。 希望本参考书目中包含的材料能够为读者指出每个主题的重要研究论文。
列表中以“Mx”的编码代表了每项的数学水平：
x=1 表示该项目不需要除微积分和线性代数以外的任何数学（然而那本是大名鼎鼎的《线性代数及其应用》——译者注）；
x=2 表示高等本科数学（微分方程、概率论、数值分析、傅里叶变换等)；
x=3 表示研究生水平（通常这意味着泛函分析——这很模糊，因为数学系本科就讲泛函了，研究生还要再讲。译者注）。
- Linear Algebra and its Applications Gilbert Strang. Harcourt Brace Jovanovich Inc., Fort Worth, third edition, 1988.
【M1】 略高于导论课程级别的线性代数教材，大名鼎鼎。对SVD（奇异值分解）的内容讲得不错。 Exercises.
- Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements S. Twomey. Elsevier, Amsterdam, 1977.
【M1.5】 数学背景，求积法(quadrature)，Tikhonov正则化，例子。最近由Dover再版。No exercises.
- Lecture notes on nonlinear inversion and tomography: I. borehole siesmic tomography James G. Berryman. See http://sepwww.stanford.edu/sep/berryman/NOTES/lecture notes.html, October 1991.
【M2】地震反演（seismic inversion），旅行时反演（ traveltime inversion）和X线断层照相术（tomography）。Exercises.
- Imaging the Earth's Interior Jon F. Claebourt. Blackwell Scientific Publications, Palo Alto, CA, 1985. Out of print, but available on the web. See http://sepwww.stanford.edu/sep/prof/index.html.
【M2】地震反演（seismic inversion） No exercises. 在此网站中还有作者Claerbout的其他的书。 译者注：大佬的学术网页做的是真好，这点国内似乎就要差一些了，嗯。
- Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data Steven C. Constable, Robert L. Parker, and Catherine G. Constable. Geophysics, 52(3):289–300, 1987.
【M2】 本文描述了一种”利用线性化问题+偏差原理（discrepancy principle）“求解非线性离散逆问题的迭代方法。
- Inverse Problems in the Mathematical Sciences Charles W. Groetsch. Vieweg, Bruanschweig; Wiesbaden, 1993.
【M2】 An introduction to the mathematics of inverse problems, requiring only undergraduate mathematics. Integral equations of the first kind, parameter estimation in differentional equations, regularization, iterative methods, the maximum entropy method, the Backus-Gilbert method. Exercises.
- Analysis of discrete ill-posed problems by means of the L-curve Per Christian Hansen. SIAM Review, 34(4):561–580, December 1992.
【M2】 本文讨论了如何使用L-曲线准则（L-curve criteria）挑选正则参数，并和广义交叉验证（generalized cross validation）作比较。
- Regularization tools: A MATLAB package for analysis and solution of discrete ill–posed problems Per Christian Hansen. Numerical Algorithms, 6:1–35, 1994. See http://www.imm.dtu.dk/documents/users/pch/Regutools/regutools.html
【M2】 正则化工具箱，提供了诸如：SVD，广义SVD，截断SVD解，Tikhonov正则化，最大熵正则化（maximum entropy regularization）等众多求解逆问题的函数（功能）。例子多，速来。
- Rank–Deficient and Discrete Ill-Posed Problems Per Christian Hansen. SIAM, Philadelphia, 1998.
【M2】 Numerical methods for discretized inverse problems, including basic theory, direct and iterative methods for regularization, and methods for picking the regularization parameter. Examples drawn from the author's regularization toolbox. No Exercises.
- Solving Least Squares Problems C. L. Lawson and R. J. Hanson. Prentice-Hall, Englewood Cliffs, New Jersey, 1974.
【M2】 关于线性最小二乘问题求解，经典书目，已由SIAM再版。包含了对L-曲线的早期讨论（毕竟是1974年的书了）。 Exercises.
- Inversion of Geophysical Data Laurence R. Lines, editor. Society of Exploration Geophysicists, 1988.
【M2】 A collection of reprints of tutorial/survey papers on inversion. Linearized inversion techniques, seismic inversion, inversion of electromagnetic and potential field data. No exercises
- Geophysical Data Analysis: Revised Edition, volume 45 of International Geophysics Series William Menke. Academic Press, San Diego, 1989.
【M2】 Generalized inverses, maximum likelihood methods, the method of Backus and Gilbert, nonlinear inverse problems, numerical algorithms, applications. No exercises.
- Geophysical Inverse Theory Robert L. Parker. Princeton University Press, Princeton, NJ, 1994.
【M2】 Mathematical background, examples from geophsyics, Tikhonov regularization, resolution, nonlinear problems. Exercises.
- Theory of seismic imaging John Scales. See http://landau.Mines.EDU/ samizdat/imaging/index.html, 1997.
【M2】 Seismic inversion, Kirchoff migration, ray tracing, finite difference methods. Exercises
- DRAFT: Geophysical inverse theory John Scales and Martin Smith. See http://landau.Mines.EDU/ samizdat/inverse theory/, 1997.
【M2】 提出（Presents）了逆问题的Bayesian方法（Bayesian approach）。 Exercises.
- A practical examination of some numerical methods for linear discrete ill-posed problems J. M. Varah. SIAM Review, 21:100–111, 1979.
【M2】 This paper compares a variety of methods for solving discrete linear inverse problems. [Wah90] Grace Wahba. Spline Models for Observational Data. SIAM, Philadelphia, 1990.
- A Primer on Integral Equations of the First Kind G. Milton Wing. SIAM, Philadelphia, 1991.
【M2】 本书介绍了第一类积分方程实际解法(practial solution)的理论方法(theory and methods)。
- Uniqueness in the inversion of inaccurate gross Earth data G. Backus and F. Gilbert. Philosophical Transactions of the Royal Society A, 266:123–192, 1970.
【M2.5】线性逆问题 (linear inverse problems) 中Backus和 Gilbert 方法的经典文章.
- Inverse Problems and Tomography in Acoustics and Seismology Philip Carrion. Penn Publishing Company, Atlanta, Georgia, 1987.
【M2.5】地震反演（seismic inversion）和X线断层照相术（tomography）。 No exercises.
- Regularization methods for the stable solution of inverse problems Heinz W. Engl. Surveys on Mathematics for Industry, 3:71–143, 1993.
【M2.5】 正则化方法的广度调查，例子多，速来。
- Regularization methods for large–scale problems. Surveys on Mathematics for Industry Martin Hanke and Per Christian Hansen. 3:253– 315, 1993.
【M2.5】 Another survey paper, with special emphasis on iterative methods for large scale problems. Contains a good discussion of methods for selecting the regularization parameter.
- Methods of Inverse Problems in Physics Dilip N. Ghosh Roy. CRC Press, Boca Raton, 1991.
【M2.5】 物理中的逆问题，Povzner-Levitan变换，Gelfand-Levitan方程，Jost函数，Marcenko积分方程Radon变换。No exercises.
- Inverse Problems: An Interdisciplinary Study P.C. Sabatier, editor. Academic Press, London, 1987.
【M2.5】 A collection of papers, mostly applications in tomography, electromagnetic inverse scattering, quantum mechanics, and other areas. No exercises.
- Stable Solution of Inverse Problems Johann Baumeister. Vieweg, Braunschweig, 1987.
【M3】不适定问题，奇异值分解，Tikhonov正则化，线性系统的最小二乘解，卷积方程(convolution equations)，终值问题(final value problems)，参数识别。No exercises.
- Regularization of Inverse Problems Heinz W. Engl, Martin Hanke, and Andreas Neubauer. Kluwer Academic Publishers, Dordrecht, 1996.
【M3】 例子，不适定线性算子方程，Tikihonov正则化，迭代正则化方法(iterative regularization methods)，共轭梯度法，数值实现，非线性问题。No exercises.
- An Introduction to the Mathematical Theory of Inverse Problems Andreas Kirsch. Springer Verlag, New York, 1996.
【M3】 Regularization theory, Tikhonov regularization, regularization by discretization, the method of Backus and Gilbert, inverse eigenvalue problems, inverse scattering problems. Includes exercises.
- Methods for Solving Incorrectly Posed Problems V. A. Morozov. Springer-Verlag, New York, 1984.
【M3】 Pseudoinverses, regularization, methods for picking the regularization parameter, nonlinear problems. No exercises.
- Solutions of Ill-Posed Problems A. N. Tikhonov and V. Y. Arsenin. John Wiley, New York, 1977.
【M3】 Tikhonov正则化理论的终极处理(definitive treatment)。
- Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation Albert Tarantola. Elsevier, New York, 1987.
【M3】 本书描述了离散+连续逆问题的Bayesian方法（Bayesian approach）。