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Bayesian Approach to Inverse Problems

2013-03-01 Mathematics
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Release : 2013-03-01
Genre : Mathematics
Kind : eBook
Book Rating : 69X/5 ( reviews)

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Book Synopsis Bayesian Approach to Inverse Problems by : Jérôme Idier

Download or read book Bayesian Approach to Inverse Problems written by Jérôme Idier. This book was released on 2013-03-01. Available in PDF, EPUB and Kindle. Book excerpt: Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.

Handbook of Uncertainty Quantification

2016-05-08 Mathematics
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Release : 2016-05-08
Genre : Mathematics
Kind : eBook
Book Rating : 844/5 ( reviews)

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Book Synopsis Handbook of Uncertainty Quantification by : Roger Ghanem

Download or read book Handbook of Uncertainty Quantification written by Roger Ghanem. This book was released on 2016-05-08. Available in PDF, EPUB and Kindle. Book excerpt: The topic of Uncertainty Quantification (UQ) has witnessed massive developments in response to the promise of achieving risk mitigation through scientific prediction. It has led to the integration of ideas from mathematics, statistics and engineering being used to lend credence to predictive assessments of risk but also to design actions (by engineers, scientists and investors) that are consistent with risk aversion. The objective of this Handbook is to facilitate the dissemination of the forefront of UQ ideas to their audiences. We recognize that these audiences are varied, with interests ranging from theory to application, and from research to development and even execution.

Bayesian Inverse Problems

2021-11-11 Mathematics
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Release : 2021-11-11
Genre : Mathematics
Kind : eBook
Book Rating : 663/5 ( reviews)

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Book Synopsis Bayesian Inverse Problems by : Juan Chiachio-Ruano

Download or read book Bayesian Inverse Problems written by Juan Chiachio-Ruano. This book was released on 2021-11-11. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a special class of engineering problems called Bayesian inverse problems. These problems comprise not only the probabilistic Bayesian formulation of engineering problems, but also the associated stochastic simulation methods needed to solve them. Through this book, the reader will learn how this class of methods can be useful to rigorously address a range of engineering problems where empirical data and fundamental knowledge come into play. The book is written for a non-expert audience and it is contributed to by many of the most renowned academic experts in this field.

Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing

2015-02-02 Technology & Engineering
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Release : 2015-02-02
Genre : Technology & Engineering
Kind : eBook
Book Rating : 981/5 ( reviews)

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Book Synopsis Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing by : Jean-Francois Giovannelli

Download or read book Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing written by Jean-Francois Giovannelli. This book was released on 2015-02-02. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this book is on "ill-posed inverse problems". These problems cannot be solved only on the basis of observed data. The building of solutions involves the recognition of other pieces of a priori information. These solutions are then specific to the pieces of information taken into account. Clarifying and taking these pieces of information into account is necessary for grasping the domain of validity and the field of application for the solutions built. For too long, the interest in these problems has remained very limited in the signal-image community. However, the community has since recognized that these matters are more interesting and they have become the subject of much greater enthusiasm. From the application field’s point of view, a significant part of the book is devoted to conventional subjects in the field of inversion: biological and medical imaging, astronomy, non-destructive evaluation, processing of video sequences, target tracking, sensor networks and digital communications. The variety of chapters is also clear, when we examine the acquisition modalities at stake: conventional modalities, such as tomography and NMR, visible or infrared optical imaging, or more recent modalities such as atomic force imaging and polarized light imaging.

Parameter Estimation and Inverse Problems

2018-10-16 Science
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Release : 2018-10-16
Genre : Science
Kind : eBook
Book Rating : 232/5 ( reviews)

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Book Synopsis Parameter Estimation and Inverse Problems by : Richard C. Aster

Download or read book Parameter Estimation and Inverse Problems written by Richard C. Aster. This book was released on 2018-10-16. Available in PDF, EPUB and Kindle. Book excerpt: Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do not have an extensive mathematical background. The book is complemented by a companion website that includes MATLAB codes that correspond to examples that are illustrated with simple, easy to follow problems that illuminate the details of particular numerical methods. Updates to the new edition include more discussions of Laplacian smoothing, an expansion of basis function exercises, the addition of stochastic descent, an improved presentation of Fourier methods and exercises, and more. Features examples that are illustrated with simple, easy to follow problems that illuminate the details of a particular numerical method Includes an online instructor’s guide that helps professors teach and customize exercises and select homework problems Covers updated information on adjoint methods that are presented in an accessible manner

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