Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
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DOI：
10.1137/1.9780898717570
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发表时间：
1987
期刊：
影响因子：
--
通讯作者：
C. Vogel
中科院分区：
文献类型：
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作者：
C. Vogel
相反，在从生物医学成像到地震勘探的许多重要的实际应用中出现了问题。这本书为读者提供了一个基本的理解都基本的数学和计算方法用于解决反问题。它还涉及像图像重建，参数识别，总变分方法，非负约束和正则化参数选择方法等专业主题。由于反问题通常涉及基于间接测量的某些量的估计，估计过程通常是不适定的。正则化方法，这已经发展到处理这种不适定性，仔细解释在前面的章节计算方法反问题。这本书还将数学和统计理论与应用和实际计算方法相结合，包括最大似然估计和贝叶斯估计等主题。几个基于网络的资源可以使这本专著互动，包括MATLAB的m文件用于生成许多例子和数字的集合。
In verse problems arise in a number of important practical applications, ranging from biomedical imaging to seismic prospecting. This book provides the reader with a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems. It also addresses specialized topics like image reconstruction, parameter identification, total variation methods, nonnegativity constraints, and regularization parameter selection methods. Because inverse problems typically involve the estimation of certain quantities based on indirect measurements, the estimation process is often ill-posed. Regularization methods, which have been developed to deal with this ill-posedness, are carefully explained in the early chapters of Computational Methods for Inverse Problems. The book also integrates mathematical and statistical theory with applications and practical computational methods, including topics like maximum likelihood estimation and Bayesian estimation. Several web-based resources are available to make this monograph interactive, including a collection of MATLAB m-files used to generate many of the examples and figures.