The Method of Approximate Inverse: Theory and Applications
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...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2007, 2007
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| Edition: | 1st ed. 2007 |
| Series: | Lecture Notes in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Inverse and Semi-discrete Problems
- Ill-posed problems and regularization methods
- Approximate inverse in L 2-spaces
- Approximate inverse in Hilbert spaces
- Approximate inverse in distribution spaces
- Conclusion and perspectives
- Application to 3D Doppler Tomography
- A semi-discrete setup for Doppler tomography
- Solving the semi-discrete problem
- Convergence and stability
- Approaches for defect correction
- Conclusion and perspectives
- Application to the spherical mean operator
- The spherical mean operator
- Design of a mollifier
- Computation of reconstruction kernels
- Numerical experiments
- Conclusion and perspectives
- Further Applications
- Approximate inverse and X-ray diffractometry
- A filtered backprojection algorithm
- Computation of reconstruction kernels in 3D computerized tomography
- Conclusion and perspectives