The Method of Approximate Inverse: Theory and Applications

• Main Author: Schuster, Thomas (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
• Series: Lecture Notes in Mathematics, 1906
• Subjects: Mathematics.; Matrix theory.; Algebra.; Integral equations.; Partial differential equations.; Numerical analysis.; Linear and Multilinear Algebras, Matrix Theory.; Partial Differential Equations.; Integral Equations.; Numerical Analysis.

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...

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.