Vogel C.R. — Computational Methods for Inverse Problems (Frontiers in Applied Mathematics) :: Электронная библиотека попечительского совета мехмата МГУ

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Vogel C.R. — Computational Methods for Inverse Problems (Frontiers in Applied Mathematics)

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Название: Computational Methods for Inverse Problems (Frontiers in Applied Mathematics)

Автор: Vogel C.R.

Аннотация:

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.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 183

Добавлена в каталог: 31.10.2010

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Предметный указатель

$C_{L}$ method      98
Active set      155
Asymptotic equality      114
Autocorrelation      50
Bayes’ Law      48
Best linear unbiased estimator      51
BFGS method      36
BFGS method, limited memory      36
Big “O” notation      114
Binding set      162
Bounded variation      147
Circulant, block matrix      72
Circulant, matrix      68
Circulant, right shift matrix      69
Compact operator      17
Complementarity      155
Complementarity for nonnegativity      156
Complementarity, strict      155
Condition number      30
Conditional, expectation      47
Conditional, probability      47
Conjugate gradient method, linear      31
Conjugate gradient method, nonlinear      34
Conjugate gradient method, preconditioned      33
Conjugate, functional      136
Conjugate, set      136
Convergence rate, linear      29
Convergence rate, quadratic      29
Convergence rate, superlinear      29
Convex, functional      21
Convex, projection      155
Convex, set      21
Convolution theorem      60
Convolution, continuous one-dimensional      1
Convolution, continuous two-dimensional      59
Convolution, discrete one-dimensional      64
Convolution, discrete two-dimensional      65
Covariance      45
Cross correlation      50
Cumulative distribution function      42
Deblurring      59
Degenerate critical point      156
Descent direction      30
Dirichlet boundary conditions      75
Discrepancy principle      8 104
Distributed parameter system      86
Divergence      145
Dual representation      137
EMLS algorithm      166
Energy, inner product      30
Energy, norm      30
entropy      25
Estimation error      97
Expectation maximization algorithm      54 165
Expected value      45
Face      160
Fast Fourier Transform      66
Fast Fourier transform, two-dimensional      67
Feasible, point      154
Feasible, set      154
Fenchel transform      136
Filter function      3
Finite element method      90
Fourier, continuous transform      60 181 182
Fourier, discrete one-dimensional transform      64
Fourier, discrete two-dimensional transform      65
Fourier, matrix      64
Frechet derivative      22
Fredholm first kind integral equation      1
Free variables      155
Frobenius      14
Galerkin’s method      90
Gateaux derivative      22
Gauss — Markov theorem      51
Gauss — Newton approximation      89
Gaussian distribution      45
Generalized cross validation      103
Generalized inverse      18
Globalization      35
Gradient      22
Gradient projection conjugate gradient method      161
Gradient projection method      157
Gram matrix      16
harmonic oscillator      85
hessian      24
Huber function      132
Ill-posed equation      16
Inactive set      155
Independence      44
Influence matrix      98 110
Karush — Kuhn — Tucker conditions      155

Kullback-Leibler information divergence      25
L-curve      106
Lagged diffusivity fixed point iteration      135
Lagrange multiplier      155
Landweber iteration      10
Laplacian, discrete      74
Least squares solution      19
Levenberg — Marquardt method      89
lexicographical ordering      71
Likelihood function      46
Line search      30
Line search, inexact      36
Line search, projected      158
Line search, quadratic backtracking      38
Linear independence constraint qualification      155
Load vector      91
Log likelihood function      46
Maximum a posteriori estimator      48
Maximum likelihood estimator      46
Mean      45
Mean squared predictive error      98
Minimum bound method      107
Modified residual norm steepest descent algorithm      169
Neumann boundary conditions      75
Newton’s method      34
Nondegenerate critical point      156
Nonnegativity constraints      151
Normal equations      76
Order optimal      8
Orthonormal      16
Output least squares      86 87
Parameter identification      85
Penalty functional      24
Periodic extension in one dimension      64
Periodic extension in two dimensions      65
Point spread function      59
Poisson distribution      45
Positive, definite      14
Positive, semidefinite      14
Predictive error      97 110
Predictive risk      98
Primal-dual Newton method      136
Prior      49
Probability, density function      42
Probability, joint      46
Probability, marginal      46
Probability, mass function      42
Probability, space      41
Projected gradient      156
Projected Newton method      158
Pseudo-inverse      18
Random variable      42
Randomized trace estimate      101
Rank      18
Reduced Hessian      159
Regular point      155
Regularization, functional      24
Regularization, generalized Tikhonov      24
Regularization, parameter      5
Regularized residual      99
Richardson — Lucy iteration      165
Sample space      41
Saturation      119
Self-adjoint operator      14
Singular system      17
Singular value decomposition      3 18
Source condition      7
State, equation      86
State, variable      85
Steepest descent method      30
Stiffness matrix      91
Strong positivity      14
Symmetric, positive definite      29
System parameters      85
Tensor product      72
Tikhonov      5
Toeplitz, block matrix      71
Toeplitz, matrix      68
Total variation      9 129
Trace      50
Trace Lemma      98
Truncated singular value decomposition      5
Trust region      35
Unbiased predictive risk estimator      99
Unbiased predictive risk estimator method      98
Uniform distribution      43
Weak, convergence      21
Weak, lower semicontinuity      21
Well-posed equation      16
White noise      98
Wolfe conditions      37

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