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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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 assume CG iterations Chapter components compute conjugate constrained minimization convergence rate corresponding define denotes derivative diagonal discrepancy principle discrete distribution eigenvalues estimation error Euclidean norm Example Exercise expected value Figure finite first fixed Fourier ftrue given grad J(f gradient projection Hessian Hilbert space ill-posed initial guess inner product inverse problems iterative solution error L-curve least squares least squares functional likelihood function line search linear operator linear systems lower semicontinuous matrix minimization problem Newton’s method nonlinear nonnegatively constrained numerical obtain one-dimensional test optimization penalty functional Poisson preconditioner predictive risk primal-dual Newton probability mass function quadratic random variable random vector Range(K reconstruction regularized solution representation right-hand side singular values solve steepest descent strictly convex subplot techniques test problem Theorem Tikhonov regularization Toeplitz total variation total variation regularization TSVD regularization TV(f two-dimensional