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In this volume selected papers delivered at the special sessions on "Inverse problems" and "Tomography and image processing" are published. These sessions were organized by A. G. Ramm at the first international congress ofISAAC (International Society for Analysis, Appli cations and Computing) which was held at the University of Delaware, June 3-7, 1997. The papers in this volume deal with a wide variety of problems including some theoretical and nu merical problems arising in various inverse problems of interest in applications (Athanasiadis, Ramm and Stratis, Crosta, Gutman, Kamimura, Kochikov, Kuramshina and Yagola, Ramm, Yakhno, Yamamoto), in tomography (Faridani, Katsevich, Sharafutdinov), and in image pro cessing (Lina, Schempp, Lobel, Pichot, Feraud and Barlaud, Weaver) These papers will be of interest to a wide audience including mathematicians, physicists, persons working in medical imaging, and theoretically oriented engineers. A.G.Ramm Manhattan, KS v CONTENTS 1. Inverse Acoustic Scattering by a Layered Obstacle C. Athanasiadis, A. G. Rarnrn, and I. G. Stratis 2. Scalar and Vector Backpropagation Applied to Shape Identification from Experimental Data: Recent Results and Open Problems .............. 9 Giovanni F. Crosta 3. Sampling in Parallel-Beam Tomography 33 Adel Faridani 4. Multidimensional Inverse Scattering Problem with Non-Reflecting Boundary Conditions ....................................... 55 Semion Gutman 5. Local Tomography with Nonsmooth Attenuation II 73 Alexander Katsevich 6. Inverse Problems of Determining Nonlinear Terms in Ordinary Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 87 . . . . . . . . Yutaka Kamimura 7. Complex Daubechies Wavelets: Filters Design and Applications 95 J.-M. Lina 8. Edge-Preserving Regularization for Quantitative Reconstruction Algorithms in Microwave Imaging . . . . . . . . . . . . . . . . . . . . . . . . .. . . 113 . . . . . . .
List of contents
1. Inverse Acoustic Scattering by a Layered Obstacle.- 2. Scalar and Vector Backpropagation Applied to Shape Identification from Experimental Data: Recent Results and Open Problems.- 3. Sampling in Parallel-Beam Tomography.- 4. Multidimensional Inverse Scattering Problem with Non-Reflecting Boundary Conditions.- 5. Local Tomography with Nonsmooth Attenuation II.- 6. Inverse Problems of Determining Nonlinear Terms in Ordinary Differential Equations.- 7. Complex Daubechies Wavelets: Filters Design and Applications.- 8. Edge-Preserving Regularization for Quantitative Reconstruction Algorithms in Microwave Imaging.- 9. On S. Saitoh's Characterization of the Range of Linear Transforms.- 10. Wavelet Modelling of Clinical Magnetic Resonance Tomography: An Ensemble Quantum Computing Approach.- 11. Ray Transform of Symmetric Tensor Fields for a Spherically Symmetric Metric.- 12. Reducing Noise in Images by Forcing Monotonic Change Between Extrema.- 13. Applied Nonlinear Ill-Posed Problems and the Variational Approach for Constructing of Regularizing Algorithms.- 14. Inverse Problem for Differential Equations System of Electromagnetoelasticity in Linear Approximation.- 15. On an Inverse Problem of Determining Source Terms in Maxwell's Equations with a Single Measurement.
