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Schuster T. — The Method of Approximate Inverse: Theory and Applications
Schuster T. — The Method of Approximate Inverse: Theory and Applications

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Название: The Method of Approximate Inverse: Theory and Applications

Автор: Schuster T.

Аннотация:

Inverse problems arise whenever one tries to calculate a required quantity from given measurements of a second quantity that is associated to the first one. Besides medical imaging and non-destructive testing, inverse problems also play an increasing role in other disciplines such as industrial and financial mathematics. Hence, there is a need for stable and efficient solvers. The book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings such as L2-spaces, Hilbert spaces or spaces of distributions. The performance and functionality of the method is demonstrated on several examples from medical imaging and non-destructive testing such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography. The book addresses graduate students and researchers interested in the numerical analysis of inverse problems and regularization techniques or in efficient solvers for the applications mentioned above.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 198

Добавлена в каталог: 13.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Approximate inverse      22 105 120 139 149 153 165 171
Approximate inverse, continuous      14 17
Approximate inverse, distributional      41 109 118
Approximate inverse, semi-discrete      30 46 47 63 74 76 77 85 94 121 139 155
Backprojection      18 116 175
Born approximation      112
Bragg angle      152 163
Center set      109
Computerized tomography      VII 149 181
Cone beam transform      181
Crofton symbol      184
Cut-off function      134
Defect      89
Diffractometry      149 151 153
Doppler effect      53
Doppler shift      55
Doppler tomography      53 74 105
Doppler transform      53 56 58 60 74 85
Energy deposition      167
Expansion equation      167
Filtered backprojection      23 77 87 149 165 175
Fourier slice theorem      20 70
Gaussian function      12
Generalized inverse      6
Gramian matrix      32 33
Grangeat’s formula      183
Helmholtz decomposition      89 90
Ill-posed problem      5
Interpolation operator      64
Inverse problem      3
Irrotational part      90
Lambda tomography      23
Laplace transform      153
Laplace transform, reciprocal      153
Laplace transform, semi-discrete      154
Lavrentiev’s method      158
Lippmann — Schwinger equation      187
Mollifier      12 40 94 119 155
Mollifier, operator      65 67
Mollifier, property      27 44 68
Observation operator      25 44 59 85 86 120 140
Orthogonal projection      6
Projection method      16
Radon transform      17 70 183
Radon transform, spherical      39
Reconstruction kernel      14 41 66 133
Refraction index      112
Regularization method      VII
Regularization method, optimal      9 87
Regularization method, order optimal      9
Regularization, method      7
Regularization, parameter      7 66 84
Regularization, Tikhonov — Phillips      7
Riesz potential      18
Riesz system      27 63 67 77
SAR      109 112 119
Singular value decomposition      7 89
Singular value decomposition, truncated      7
Solenoidal part      90
Sonar      109 112 119
Spherical mean operator      39 109 113 115 165
Tempered distribution      113
Thermoacoustic CT      149 165
Thermoelastic effect      167
Tuy — Kirillov condition      184
Velocity spectrum      55 90
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