Discrete Inverse Problems

Insight and Algorithms

AvPer Christian Hansen

Häftad, Engelska, 2010

Del i serien Fundamentals of Algorithms

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Beskrivning

Inverse problems arise when we reconstruct a sharper image from a blurred one or reconstruct the underground mass density from measurements of the gravity above the ground. When we solve an inverse problem, we compute the source that gives rise to some observed data using a mathematical model for the relation between the source and the data.This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.Discrete Inverse Problems includes a number of tutorial exercises that give the reader hands-on experience with the methods, difficulties, and challenges associated with the treatment of inverse problems. It also includes examples and figures that illustrate the theory and algorithms.

Produktinformation

Utgivningsdatum:2010-02-28
Mått:152 x 229 x 15 mm
Vikt:427 g
Format:Häftad
Språk:Engelska
Serie:Fundamentals of Algorithms
Antal sidor:225
Förlag:Society for Industrial & Applied Mathematics,U.S.
ISBN:9780898716962

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Mer om författaren

Per Christian Hansen is Professor of Scientific Computing at the Technical University of Denmark. His publications include two other books on inverse problems, several MATLAB packages, and many papers on inverse problems, matrix computations, and signal processing.

Innehållsförteckning

PrefaceList of SymbolsChapter 1: Introduction and MotivationChapter 2: Meet the Fredholm Integral Equation of the First KindChapter 3: Getting to Business: Discretizations of Linear Inverse ProblemsChapter 4: Computational Aspects: Regularization MethodsChapter 5: Getting Serious: Choosing the Regularization ParameterChapter 6: Toward Real-World Problems: Iterative RegularizationChapter 7: Regularization Methods at Work: Solving Real ProblemsChapter 8: Beyond the 2-Norm: The Use of Discrete Smoothing NormsAppendix A: Linear Algebra StuffAppendix B: Symmetric Toeplitz-Plus-Hankel Matrices and the DCTAppendix C: Early Work on “Tikhonov Regularization”BibliographyIndex