This book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings. It demonstrates the performance and functionality of the method on several examples from medical imaging and non-destructive testing, such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography.
Table of Content
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.
About the author
1990 – 1995 Study of Mathematics at Saarland University Saarbrücken (Germany)1996 – 2004 Scientific assistant at Saarland University Saarbrücken (Germany)1999 Ph D at Saarland University Saarbrücken (Germany)2002 – 2003 Research stay at Tufts University Medford, MA (USA)2004 Habilitation at Saarland University Saarbrücken (Germany)2004 – 2006 Assistant Professor at Saarland University Saarbrücken (Germany)2007 – today Associate Professor at the Helmut Schmidt University Hamburg (Germany)
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