Atjaunināt sīkdatņu piekrišanu

Discrete Inverse Problems: Insight and Algorithms [Paperback]

4.00/5 (6 ratings by Goodreads)
  • Formāts: Paperback, 225 pages, height x width x depth: 229x152x12 mm, weight: 420 g, illustrations
  • Sērija : Fundamentals of Algorithms
  • Izdošanas datums: 28-Feb-2010
  • Izdevniecība: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898716969
  • ISBN-13: 9780898716962
Citas grāmatas par šo tēmu:
  • Paperback
  • Cena: 91,78 €
  • Grāmatu piegādes laiks ir 3-4 nedēļas, ja grāmata ir uz vietas izdevniecības noliktavā. Ja izdevējam nepieciešams publicēt jaunu tirāžu, grāmatas piegāde var aizkavēties.
  • Daudzums:
  • Ielikt grozā
  • Piegādes laiks - 4-6 nedēļas
  • Pievienot vēlmju sarakstam
Discrete Inverse Problems: Insight and AlgorithmsPalielināt
  • Formāts: Paperback, 225 pages, height x width x depth: 229x152x12 mm, weight: 420 g, illustrations
  • Sērija : Fundamentals of Algorithms
  • Izdošanas datums: 28-Feb-2010
  • Izdevniecība: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898716969
  • ISBN-13: 9780898716962
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780898716962.html
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.
Preface ix
List of Symbols
xi
Introduction and Motivation
1(4)
Meet the Fredholm Integral Equation of the First Kind
5(18)
A Model Problem from Geophysics
5(2)
Properties of the Integral Equation
7(3)
The Singular Value Expansion and the Picard Condition
10(5)
The Role of the SVE
10(3)
Nonexistence of a Solution
13(1)
Nitty-Gritty Details of the SVE
14(1)
Ambiguity in Inverse Problems
15(2)
Spectral Properties of the Singular Functions
17(3)
The Story So Far
20(1)
Exercises
20(3)
Getting to Business: Discretizations of Linear Inverse Problems
23(30)
Quadrature and Expansion Methods
23(5)
Quadrature Methods
24(1)
Expansion Methods
25(2)
Which Method to Choose?
27(1)
The Singular Value Decomposition
28(5)
The Role of the SVD
30(1)
Symmetries
31(1)
Nitty-Gritty Details of the SVD
32(1)
SVD Analysis and the Discrete Picard Condition
33(4)
Convergence and Nonconvergence of SVE Approximation
37(2)
A Closer Look at Data with White Noise
39(4)
Gaussian White Noise
41(1)
Uniformly Distributed White Noise
42(1)
Noise that Is Not White
43(4)
Signal-Correlated Noise
43(1)
Poisson Noise
44(2)
Broad-Band Colored Noise
46(1)
The Story So Far
47(1)
Exercises
48(5)
Computational Aspects: Regularization Methods
53(32)
The Need for Regularization
54(1)
Truncated SVD
55(3)
Selective SVD
58(2)
Tikhonov Regularization
60(4)
Perturbation Theory
64(4)
The Role of the Discrete Picard Condition
68(3)
The L-Curve
71(3)
When the Noise Is Not White---Regularization Aspects
74(3)
Dealing with HF and LF Noise
74(1)
Good Old Prewhitening
75(2)
Rank-Deficient Problems → Different Creatures
77(2)
The Story So Far
79(1)
Exercises
79(6)
Getting Serious: Choosing the Regularization Parameter
85(24)
Regularization Errors and Perturbation Errors
86(3)
Simplicity: The Discrepancy Principle
89(2)
The Intuitive L-Curve Criterion
91(4)
The Statistician's Choice---Generalized Cross Validation
95(3)
Squeezing the Most Out of the Residual Vector---NCP Analysis
98(3)
Comparison of the Methods
101(4)
The Story So Far
105(1)
Exercises
105(4)
Toward Real-World Problems: Iterative Regularization
109(26)
A Few Stationary Iterative Methods
110(4)
Landweber and Cimmino Iteration
111(2)
ART a.k.a. Kaczmarz's Method
113(1)
Projection Methods
114(4)
Regularizing Krylov-Subspace Iterations
118(8)
The Krylov Subspace
119(2)
The CGLS Algorithm
121(2)
CGLS Focuses on the Significant Components
123(1)
Other Iterations---MR-II and RRGMRES
124(2)
Projection + Regularization = Best of Both Worlds
126(4)
The Story So Far
130(1)
Exercises
131(4)
Regularization Methods at Work: Solving Real Problems
135(36)
Barcode Reading---Deconvolution at Work
135(4)
Discrete Convolution
137(1)
Condition Number of a Gaussian Toeplitz Matrix
138(1)
Inverse Crime---Ignoring Data/Model Mismatch
139(1)
The Importance of Boundary Conditions
140(2)
Taking Advantage of Matrix Structure
142(2)
Deconvolution in 2D---Image Deblurring
144(5)
The Role of the Point Spread Function
146(2)
Rank-One PSF Arrays and Fast Algorithms
148(1)
Deconvolution and Resolution
149(3)
Tomography in 2D
152(2)
Depth Profiling and Depth Resolution
154(3)
Digging Deeper---2D Gravity Surveying
157(3)
Working Regularization Algorithms
160(3)
The Story So Far
163(1)
Exercises
164(7)
Beyond the 2-Norm: The Use of Discrete Smoothing Norms
171(34)
Tikhonov Regularization in General Form
171(4)
A Catalogue of Derivative Matrices
175(2)
The Generalized SVD
177(4)
Standard-Form Transformation and Smoothing Preconditioning
181(2)
The Quest for the Standard-Form Transformation
183(4)
Oblique Projections
184(2)
Splitting of the Beast
186(1)
Prelude to Total Variation Regularization
187(4)
And the Story Continues
191(1)
Exercises
192(3)
Appendix
Linear Algebra Stuff
195(4)
Symmetric Toeplitz-Plus-Hankel Matrices and the DCT
199(4)
Early Work on ``Tikhonov Regularization''
203(2)
Bibliography 205(6)
Index 211
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.