An Introduction to Inverse Problems with Applications

An Introduction to Inverse Problems with Applications
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There is an obvious need to synthesize the various approaches and to provide textbooks that explain the subject from different points of view while being accessible to students who may have a limited mathematical or statistical background. The authors of this book are respectively a mathematician and an engineer.

Introduction to inverse problems - Lakshmivarahan

Their book attempts to introduce the subject of inverse problems in a way that emphasizes practical methods for the solution of applied problems while also providing a general understanding of the subject. In order to make the book accessible to scientists and engineers, the authors have assumed that readers are familiar only with mathematics to the level of calculus, linear algebra, and differential equations.

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This makes it among the most accessible textbooks on the subject. The book begins with a set of three introductory chapters that provide an introduction to mathematical modeling and inverse problems.

1 Introduction

Computational engineering/science uses a blend of applications, mathematical models and computations. Mathematical models require accurate. Buy An Introduction to Inverse Problems with Applications on ✓ FREE SHIPPING on qualified orders.

After this introduction the authors give a concise development of the spectral theory of discrete linear inverse problems and Tikhonov regularization. This chapter also includes several iterative methods for the regularization of discrete linear inverse problems including the Landweber iteration and the conjugate gradient method. The second half of the book consists of largely self contained chapters on particular inverse problems, including applications to image restoration and heat transfer.

These chapters build on and extend the discussion of discrete linear inverse problems.

An introduction to inverse problems with applications [electronic resource] in SearchWorks catalog

For example, in the chapter on image restoration, the authors begin with Tikhonov regularization but then go on to consider maximum entropy regularization. The resulting optimization problems are nonlinear least squares problems, so the authors introduce Newton's method and the Levenberg-Marquardt method for solving nonlinear least squares problems. In a later chapter on heat conduction, the authors go beyond the discretized formulation of the problem and consider optimization over a space of functions.

They then introduce the adjoint equation and use it to obtain a gradient for use with the conjugate gradient method. This book should be of interest to instructors who want to teach an introductory course in inverse problems with limited mathematics prerequisites to an audience of scientists and engineers at the advanced undergraduate or graduate level.

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As a textbook, the strengths of this book are the extensive examples and exercises, as well as an appendix covering required mathematical background. One weakness is that the authors have not made example code available. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

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In order to stress the industrial aspects of such activities, some of the motivation and exemplification for this review is drawn from food rheology and technology, as well as industrial polymer processing. Introduction to medical imaging. Other areas of expertise include earthquake location the topic of a book he edited and geophysical inverse theory. Mathematical models require accurate approximations of their parameters, which are often viewed as solutions to inverse problems. A discussion of the several specific problems that must still be solved for obtaining accurate and efficient reconstructions is inserted at the end of this review. We expose mostly known results and some new ideas and approaches. The first approach is the so-called pixel-based inversion PBI algorithm.

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Introduction to mathematics of deep learning and applications to inverse problems

An inverse problem refers to the reconstruction of an object j? Usually, one observes a noisy transformation of j through an operator. Solving an inverse problem consists in inverting such an operator, which may be challenging if the inverse problem is ill-posed. Ill-posed inverse problems arise in many applications in many fields. In structural econometrics, the importance of the theory of inverse problems has considerably increased over the last fifteen years.