Computational Methods for Inverse ProblemsSIAM, 1 Oca 2002 - 199 sayfa Inverse 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. |
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FR23ch1 | 1 |
FR23ch2 | 13 |
FR23ch3 | 29 |
FR23ch4 | 41 |
FR23ch5 | 59 |
FR23ch6 | 85 |
FR23ch7 | 97 |
FR23ch8 | 129 |
FR23ch9 | 151 |
FR23bm | 173 |
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Algorithm analysis applied approximation assume assumption block boundary bounded called Chapter circulant components compute Consider constrained continuous convergence convex corresponding cost defined Definition denotes derivative differentiable direction discrete distribution equality equation error estimation Example Exercise exists expected expressed Figure filter fixed Fourier frue functional given grad gradient Hence Hessian implementation indicate initial inverse iteration least squares likelihood line search linear linear systems matrix mean method minimizer Newton noise nonnegatively norm Note numerical obtain one-dimensional operator optimization penalty positive preconditioner predictive presented probability problem projection Proof Proposition Prove random vector reconstruction regularization parameter Remark replace representation represents requires selection singular solution solve space techniques term Theorem Tikhonov regularization TSVD two-dimensional variation vector yields zero