Ramm A.G. (ed.) Inverse Problems, Tomography, and Image Processing

New York: Springer, 1998. — 262 p.The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, in all areas of today's Physical Sciences and Engineering, is well established. The purpose of the sets of volumes, the present one being the first in a planned series of sequential sets, is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume in each set will provide a detailed introduction to a specific subject area of current importance, and then goes beyond this by reviewing recent contributions, thereby serving as a valuable reference source.
The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems in modern Physical Sciences and Engineering would otherwise have been impossible.
A case in point is the analytical technique of singular perturbation theory (Volume 3), which has a long history. In recent years it has been used in many different ways, and its importance has been enhanced by its having been used in various fields to derive sequences of asymptotic approximations, each with a higher order of accuracy than its predecessor. These approximations have, in turn, provided a better understanding of the subject and stimulated the development of new methods for the numerical solution of the higher order approximations. A typical example of this type is to be found in the general study of nonlinear wave propagation phenomena as typified by the study of water waves.Inverse Acoustic Scattering by a Layered Obstacle
Scalar and Vector Backpropagation Applied to Shape Identification from Experimental Data: Recent Results and Open Problems
Sampling in Parallel-Beam Tomography
Multidimensional Inverse Scattering Problem with Non-Reflecting Boundary Conditions
Local Tomography with Nonsmooth Attenuation II
Inverse Problems of Determining Nonlinear Terms in Ordinary Differential Equations
Complex Daubechies Wavelets: Filters Design and Applications
Edge-Preserving Regularization for Quantitative Reconstruction Algorithms in Microwave Imaging
On S. Saitoh’s Characterization of the Range of Linear Transforms
Wavelet Modelling of Clinical Magnetic Resonance Tomography: An Ensemble Quantum Computing Approach
Ray Transform of Symmetric Tensor Fields for a Spherically Symmetric Metric
Reducing Noise in Images by Forcing Monotonic Change Between Extrema
Applied Nonlinear Ill-Posed Problems and the Variational Approach for Constructing of Regularizing Algorithms
Inverse Problem for Differential Equations System of Electromagnetoelasticity in Linear Approximation
On an Inverse Problem of Determining Source Terms in Maxwell’s Equations with a Single Measurement