TY  - BOOK
AU  - Schuster,Thomas
ED  - SpringerLink (Online service)
TI  - The Method of Approximate Inverse: Theory and Applications
T2  - Lecture Notes in Mathematics,
SN  - 9783540712275
AV  - QA184-205 
U1  - 512.5 23
PY  - 2007///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Matrix theory
KW  - Integral equations
KW  - Differential equations, partial
KW  - Numerical analysis
KW  - Linear and Multilinear Algebras, Matrix Theory
KW  - Partial Differential Equations
KW  - Integral Equations
KW  - Numerical Analysis
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-540-71227-5
ER  -