Inverse Problems In Physical Diagnostics
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| Author | : Konstantin P. Gaikovich |
| Publisher | : Nova Publishers |
| Total Pages | : 392 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9781594540950 |
Unlike direct problems related to the solution of differential equations, inverse problems are typically expressed by integral equations. These equations relate media parameters to parameters of a measured signal, or input parameters to output ones in various measurement systems. The solution of integral equations is, with few exceptions, an ill-posed problem, and additional a priori information about the exact solution should be used to solve such problems. The specific character of the a priori information determines various regularisation methods that are in use here to obtain an approximate solution: Tikhonov's method, statistical regularisation method, methods based on the use of additional equations or restrictions or of models with limited number of unknown parameters. The main point of this book is the study of convergence properties of each method and the wide application of numerical modelling that gives the accuracy of the solution in a chosen metric. It is an unaccustomed procedure for physicists, but, because there is no proportionality between data and solution errors in ill-posed problems, such approach is inevitable.
| Author | : Peter W. Macfarlane |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 2310 |
| Release | : 2010-11-05 |
| Genre | : Medical |
| ISBN | : 1848820453 |
New edition of the classic complete reference book for cardiologists and trainee cardiologists on the theory and practice of electrocardiography, one of the key modalities used for evaluating cardiology patients and deciding on appropriate management strategies.
| Author | : Martin Hanke |
| Publisher | : SIAM |
| Total Pages | : 171 |
| Release | : 2017-01-01 |
| Genre | : Mathematics |
| ISBN | : 1611974941 |
Inverse problems need to be solved in order to properly interpret indirect measurements. Often, inverse problems are ill-posed and sensitive to data errors. Therefore one has to incorporate some sort of regularization to reconstruct significant information from the given data. This book presents the main achievements that have emerged in regularization theory over the past 50 years, focusing on linear ill-posed problems and the development of methods that can be applied to them. Some of this material has previously appeared only in journal articles. A Taste of Inverse Problems: Basic Theory and Examples rigorously discusses state-of-the-art inverse problems theory, focusing on numerically relevant aspects and omitting subordinate generalizations;presents diverse real-world applications, important test cases, and possible pitfalls; and treats these applications with the same rigor and depth as the theory.
| Author | : Otmar Scherzer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1626 |
| Release | : 2010-11-23 |
| Genre | : Mathematics |
| ISBN | : 0387929193 |
The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
| Author | : Oleg M. Alifanov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 360 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642764363 |
This research monograph presents a systematic treatment of the theory of the propagation of transient electromagnetic fields (such as optical pulses) through dielectric media which exhibit both dispersion a.nd absorption. The work divides naturally into two parts. Part I presents a summary of the fundamental theory of the radiation and propagation of rather general electromagnetic waves in causal, linear media which are homogeneous and isotropic but which otherwise have rather general dispersive and absorbing properties. In Part II, we specialize to the propagation of a plane, transient electromagnetic field in a homogeneous dielectric. Although we have made some contributions to the fundamental theory given in Part I, most of the results of our own research appear in Part II. The purpose of the theory presented in Part II is to predict and to explain in explicit detail the dynamics of the field after it has propagated far enough through the medium to be in the mature-dispersion regime. It is the subject of a classic theory, based on the research conducted by A. Sommerfeld and L.
| Author | : James Keener |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1067 |
| Release | : 2010-06-04 |
| Genre | : Mathematics |
| ISBN | : 038775847X |
Divided into two volumes, the book begins with a pedagogical presentation of some of the basic theory, with chapters on biochemical reactions, diffusion, excitability, wave propagation and cellular homeostasis. The second, more extensive part discusses particular physiological systems, with chapters on calcium dynamics, bursting oscillations and secretion, cardiac cells, muscles, intercellular communication, the circulatory system, the immune system, wound healing, the respiratory system, the visual system, hormone physiology, renal physiology, digestion, the visual system and hearing. New chapters on Calcium Dynamics, Neuroendocrine Cells and Regulation of Cell Function have been included. Reviews from first edition: Keener and Sneyd's Mathematical Physiology is the first comprehensive text of its kind that deals exclusively with the interplay between mathematics and physiology. Writing a book like this is an audacious act! -Society of Mathematical Biology Keener and Sneyd's is unique in that it attempts to present one of the most important subfields of biology and medicine, physiology, in terms of mathematical "language", rather than organizing materials around mathematical methodology. -SIAM review
| Author | : Lídice Camps Echevarría |
| Publisher | : Springer |
| Total Pages | : 179 |
| Release | : 2018-05-28 |
| Genre | : Mathematics |
| ISBN | : 3319899783 |
This book presents a methodology based on inverse problems for use in solutions for fault diagnosis in control systems, combining tools from mathematics, physics, computational and mathematical modeling, optimization and computational intelligence. This methodology, known as fault diagnosis – inverse problem methodology or FD-IPM, unifies the results of several years of work of the authors in the fields of fault detection and isolation (FDI), inverse problems and optimization. The book clearly and systematically presents the main ideas, concepts and results obtained in recent years. By formulating fault diagnosis as an inverse problem, and by solving it using metaheuristics, the authors offer researchers and students a fresh, interdisciplinary perspective for problem solving in these fields. Graduate courses in engineering, applied mathematics and computing also benefit from this work.
| Author | : Charles W. Groetsch |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 236 |
| Release | : 1999-12-31 |
| Genre | : Mathematics |
| ISBN | : 1470448734 |
Problem solving in mathematics is often thought of as a one way process. For example: take two numbers and multiply them together. However for each problem there is also an inverse problem which runs in the opposite direction: now take a number and find a pair of factors. Such problems are considerably more important, in mathematics and throughout science, than they might first appear. This book concentrates on these inverse problems and how they can be usefully introduced to undergraduate students. A historical introduction sets the scene and gives a cultural context for the rest of the book. Chapters dealing with inverse problems in calculus, differential equations and linear algebra then follow and the book concludes with suggestions for further reading. Whatever their own field of expertise, this will be an essential purchase for anyone interested in the teaching of mathematics.
| Author | : Dilip N. Ghosh Roy |
| Publisher | : CRC Press |
| Total Pages | : 506 |
| Release | : 1991-03-14 |
| Genre | : Science |
| ISBN | : 9780849362583 |
This interesting volume focuses on the second of the two broad categories into which problems of physical sciences fall-direct (or forward) and inverse (or backward) problems. It emphasizes one-dimensional problems because of their mathematical clarity. The unique feature of the monograph is its rigorous presentation of inverse problems (from quantum scattering to vibrational systems), transmission lines, and imaging sciences in a single volume. It includes exhaustive discussions on spectral function, inverse scattering integral equations of Gel'fand-Levitan and Marcenko, Povzner-Levitan and Levin transforms, Møller wave operators and Krein's functionals, S-matrix and scattering data, and inverse scattering transform for solving nonlinear evolution equations via inverse solving of a linear, isospectral Schrodinger equation and multisoliton solutions of the K-dV equation, which are of special interest to quantum physicists and mathematicians. The book also gives an exhaustive account of inverse problems in discrete systems, including inverting a Jacobi and a Toeplitz matrix, which can be applied to geophysics, electrical engineering, applied mechanics, and mathematics. A rigorous inverse problem for a continuous transmission line developed by Brown and Wilcox is included. The book concludes with inverse problems in integral geometry, specifically Radon's transform and its inversion, which is of particular interest to imaging scientists. This fascinating volume will interest anyone involved with quantum scattering, theoretical physics, linear and nonlinear optics, geosciences, mechanical, biomedical, and electrical engineering, and imaging research.
| Author | : N.V. Korovkin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 339 |
| Release | : 2007-04-14 |
| Genre | : Technology & Engineering |
| ISBN | : 0387460470 |
This is the first book to offer a comprehensive exploration of new methods in inverse problems in electromagnetics. The book provides systematic descriptions of the most important practical inverse problems, and details new methods to solve them. Also included are descriptions of the properties of inverse problems and known solutions, as well as reviews of the practical implementation of these methods in electric circuit theory and electromagnetic fields theory. This comprehensive collection of modern theoretical ideas and methods to solve inverse problems will be of value to both students and working professionals.
