الصفحة 1
الصفحة 1
Multirate Statistical Signal Processing
This book introduces a statistical theory for extracting information from signals that have di?erent sampling rates. This new theory generalizes the conventional (deterministic) theory of multirate systems beyond many of its constraints.Furthermore,itallowsfortheformulationofseveralnewproblems such as spectrum estimation, time-delay estimation and sensor fusion in the realm of multirate signal processing. I have arrived at the theory presented here by integrating concepts from diverse areas such as information theory, inverse problems and theory of - equalities. The process of merging a variety of concepts of di?erent origin results in both merits and shortcomings. The former include the fresh and - di?erentiated view of an amateur, providing scope of application. The latter include a lack of in-depth experience in each of the original ?elds. Granted, this may lead to gaps in continuity, however it goes without saying that a complete theory can seldom be achieved by one person and in a short time.
Inverse Problems in Vibration
In this new edition the scope of the book has been widened to include topics such as isospectral systems- families of systems which all exhibit some specified behaviour; applications of the concept of Toda flow; new, non-classical approaches to inverse Sturm-Liouville problems; qualitative properties of the modes of some finite element models; damage identification.
Inverse Problems in Electric Circuits and Electromagnetics
This text treats important new methods in inverse problems in electromagnetics. The inverse problems such as synthesis, diagnostics, fault detection, and identification are becoming one of the most important subjects in the field because of the significant practical applications to electric circuits and electromagnetics. This book introduces the recent achievements in mathematics and computing, while focusing on an approach to inverse problems that provides numerical solutions. The text systematically supplies descriptions of the most important practical inverse problems and the methods to solve them, thereby providing the reader with the best application for these intuitive processes. Also included are descriptions of the properties of inverse problems and known methods of their solution as well as the practical implementation of these methods in electric circuits theory and electromagnetic field theory.
Inverse Problems for Partial Differential Equations
The topic of the inverse problems is of substantial and rapidly growing interest for many scientists and engineers. The second edition covers most important recent developments in the field of inverse problems, describing theoretical and computational methods, and emphasizing new ideas and techniques. It also reflects new changes since the first edition, including some corrections. This edition is considerably expanded, with some concepts such as pseudo-convexity, and proofs simplified. New material is added to reflect recent progress in theory of inverse problems.This book is intended for mathematicians working with partial differential equations and their applications, and physicists, geophysicists and engineers involved with experiments in nondestructive evaluation, seismic exploration, remote sensing and tomography.
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.
Introduction to Bayesian Statistics
This is the second and translated edition of the German book “Einf ̈uhrung in die Bayes-Statistik, Springer-Verlag, Berlin Heidelberg New York, 2000”. It has been completely revised and numerous new developments are pointed out together with the relevant literature. The Chapter 5.2.4 is extended by the stochastic trace estimation for variance components. The new Chapter 5.2.6 presents the estimation of the regularization parameter of type Tykhonov regularization for inverse problems as the ratio of two variance components.The reconstruction and the smoothing of digital three-dimensional images is demonstrated in the new Chapter 5.3. The Chapter 6.2.1 on importance sampling for the Monte Carlo integration is rewritten to solve a more general integral. This chapter contains also the derivation of the SIR (sampling-importance-resampling) algorithm as an alternative to the rejection method for generating random samples. Markov Chain Monte Carlo methods are now frequently applied in Bayesian statistics.
Introduction to Bayesian Scientific Computing : Ten Lectures on Subjective Computing
Inverse problems are closely related to statistical inference problems, where the observations are used to infer on an underlying probability distribution. This connection between statistical inference and inverse problems is a central topic of the book. Inverse problems are typically ill-posed: small uncertainties in data may propagate in huge uncertainties in the estimates of the unknowns. To cope with such problems, efficient regularization techniques are developed in the framework of numerical analysis. The counterpart of regularization in the framework of statistical inference is the use prior information.
Interpolation, Schur Functions and Moment Problems
In signal processing, they are often named reflection coefficients. Under the word "Schur analysis" one encounters a variety of problems related to Schur functions, such as interpolation problems, moment problems, the study of the relationships between the Schur coefficients and the properties of the function, or the study of underlying operators. Such questions are also considered for some generalizations of Schur functions. Furthermore, there is an extension of the notion of a Schur function for functions that are analytic and have a positive real part in the open upper half-plane; these functions are called Carathéodory functions. This volume is almost entirely dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes.
Image processing based on partial differential equations ; Proceedings of the International Conference on PDE-Based Image Processing and Related Inverse Problems, CMA, Oslo, August 8-12, 2005
The book contains twenty-two original scienti?c research articles that address the state-of-the-art in using partial di?erential equations for image and signal processing. The articles arose from presentations given at the inter- tional conference on PDE-Based Image Processing and Related Inverse Pr- lems, held at the Centre of Mathematics for Applications, University of Oslo, Norway, August 8-12, 2005.
Fracture Mechanics : Inverse Problems and Solutions
This book presents, in a unified manner, a variety of topics in Continuum and Fracture Mechanics: energy methods, conservation laws, mathematical methods to solve two-dimensional and three-dimensional crack problems.
Field Models in Electricity and Magnetism
Covering the development of field computation in the past forty years, Field Models in Electricity and Magnetism intends to be a concise, comprehensive and up-to-date introduction to field models in electricity and magnetism, ranging from basic theory to numerical applications. The approach assumed throughout the whole book is to solve field problems directly from partial differential equations in terms of vector quantities. Theoretical issues are illustrated by practical examples. In particular, a single example is solved by different methods so that, by comparison of results, limitations and advantages of the various methods are made clear.
Computing the Electrical Activity in the Heart
This book describes mathematical models and numerical techniques for simulating the electrical activity in the heart. The book gives an introduction to the most important models of the field, followed by a detailed description of numerical techniques for the models. Particular focus is on efficient numerical methods for large scale simulations on both scalar and parallel computers.
An Introduction to Mathematics of Emerging Biomedical Imaging
Biomedical imaging is a fascinating research area to applied mathematicians. Challenging imaging problems arise and they often trigger the investigation of fundamental problems in various branches of mathematics. This is the first book to highlight the most recent mathematical developments in emerging biomedical imaging techniques. The main focus is on emerging multi-physics and multi-scales imaging approaches. For such promising techniques, it provides the basic mathematical concepts and tools for image reconstruction. Further improvements in these exciting imaging techniques require continued research in the mathematical sciences, a field that has contributed greatly to biomedical imaging and will continue to do so.
Algebraic Analysis of Differential Equations : from Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai Editors
This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the international conference "Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. Microlocal analysis and exponential asymptotics are intimately connected and provide powerful tools that have been applied to linear and non-linear differential equations as well as many related fields such as real and complex analysis, integral transforms, spectral theory, inverse problems, integrable systems, and mathematical physics. The articles contained here present many new results and ideas, providing interested researchers and students with valuable suggestions and instructive guidance for their work.
Advances in Automatic Differentiation
Covers advances in automatic differentiation theory and practice. Computer scientists and mathematicians will learn about recent developments in automatic differentiation theory as well as mechanisms for the construction of robust and powerful automatic differentiation tools. Computational scientists and engineers will benefit from the discussion of various applications, which provide insight into effective strategies for using automatic differentiation for inverse problems and design optimization.
Acoustic sensing techniques for the shallow water environment : Inversion methods and experiments
Contains the collection of papers from the second workshop on Experimental Acoustic Inversion Techniques for Exploration of the Shallow Water Environment. Acoustic techniques provide the most effective means for remote sensing of ocean and sea floor processes, and for probing the structure beneath the sea floor. No other energy propagates as efficiently in the ocean: radio waves and visible light are severely limited in range because the ocean is a highly conductive medium. However, sound from breaking waves and coastal shipping can be heard throughout the ocean, and marine mammals communicate acoustically over basin scale distances.
