الصفحة 1
الصفحة 1
Inverse Problems and Imaging : Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy September 15–21, 2002
Nowadays we are facing numerous and important imaging problems: nondestructive testing of materials, monitoring of industrial processes, enhancement of oil production by efficient reservoir characterization, emerging developments in noninvasive imaging techniques for medical purposes - computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), X-ray and ultrasound tomography, etc. In the CIME Summer School on Imaging (Martina Franca, Italy 2002), leading experts in mathematical techniques and applications presented broad and useful introductions for non-experts and practitioners alike to many aspects of this exciting field. The volume contains part of the above lectures completed and updated by additional contributions on other related topics: a general presentation and introduction (Moscoso), X-ray tomography (Natterer), Electromagnetic imaging (Dorn, Bertete-Aguirre, Papanicolaou), coherent imaging in telecommunications in a multiple input-multiple output setup (Dorn), polarization based optical imaging (Moscoso), topological derivatives used in shape reconstruction related to inverse scattering problems (Carpio, Rapún), Point interactions (Dell’Antonio, Figari, Teta).
Inverse Problems : Mathematical and Analytical Techniques with Applications to Engineering
This book presents the theory of inverse spectral and scattering problems and of many other inverse problems for differential equations in an essentially self-contained way. An outline of the theory of ill-posed problems is given, because inverse problems are often ill-posed.
Integrable Hamiltonian Hierarchies : Spectral and Geometric Methods
This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their Hamiltonian hierarchies. Thus it is demonstrated that the inverse scattering method for solving soliton equations is a nonlinear generalization of the Fourier transform. The book brings together the spectral and the geometric approaches and as such will be useful to a wide readership: from researchers in the field of nonlinear completely integrable evolution equations to graduate and post-graduate students.
Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations
Domain decomposition methods are divide and conquer methods for the parallel and computational solution of partial differential equations of elliptic or parabolic type. They include iterative algorithms for solving the discretized equations, techniques for non-matching grid discretizations and techniques for heterogeneous approximations. This book serves as an introduction to this subject, with emphasis on matrix formulations. The topics studied include Schwarz, substructuring, Lagrange multiplier and least squares-control hybrid formulations, multilevel methods, non-self adjoint problems, parabolic equations, saddle point problems (Stokes, porous media and optimal control), non-matching grid discretizations, heterogeneous models, fictitious domain methods, variational inequalities, maximum norm theory, eigenvalue problems, optimization problems and the Helmholtz scattering problem. Selected convergence theory is included.
Direct and inverse Sturm-Liouville problems : A method of solution
This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems.
Light Scattering Reviews 3 : Light Scattering and Reflection
Ddevoted to modern knowledge and milestones in both experimental and theoretical techniques related to light scattering and radiative transport problems. It will consist of 3 parts comprising 11 contributions written by world leading experts in their respective fields. The general focus of the book will be on remote sensing of geophysical media. The first part will be devoted exclusively to studies of single light scattering by particles of different shapes and chemical compositions. The first chapter will review in situ measurements of cloud optical characteristics like cloud extinction and phase function, with the emphasis on ice clouds. Chapter 2 will cover opitcally soft particles common in marine environments and bio-suspensions while Chapter 3 will describe numerical techniques applicable not only to isotropic but also to chiral and anisotropic mdia. The final chapter in this part will deal with spatial symmetries in light scattering problems.
Light Scattering by Optically Soft Particles: Theory and Applications
Deals with a particular class of approximation methods in the context of light scattering by small particles. This class of approximations has been termed as eikonal or soft particle approximations. The eikonal approximation was studied extensively in the potential scattering and then adopted in optical scattering problems. In this context, the eikonal and other soft particle approximations pertain to scatterers whose relative refractive index compared to surrounding medium is close to unity. The study of these approximations is very important because soft particles occur abundantly in nature. For example, the particles that occur in ocean optics, biomedical optics, atmospheric optics and in many industrial applications can be classified as soft particles. This book was written in recognition of the long-standing and current interest in the field of scattering approximations for soft particles. It should prove to be a useful addition for researchers in the field of light scattering.
An Introduction to Echo Analysis : Scattering Theory and Wave Propagation
The use of various types of wave energy is an increasingly promising, non-destructive means of detecting objects and of diagnosing the properties of quite complicated materials. An analysis of this technique requires an understanding of how waves evolve in the medium of interest and how they are scattered by inhomogeneities in the medium. These scattering phenomena can be thought of as arising from some perturbation of a given, known system and they are analysed by developing a scattering theory. This monograph provides an introductory account of scattering phenomena and a guide to the technical requirements for investigating wave scattering problems.
