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Détails
| Format physique additionnel : | Online version: Byrne, C. L. (Charles L.), 1947- Applied iterative methods. Wellesley, Mass. : AK Peters, c2008 (OCoLC)763517876 |
|---|---|
| Type d’ouvrage : | Ressource Internet |
| Format : | Livre, Ressource Internet |
| Tous les auteurs / collaborateurs : |
C L Byrne |
| ISBN : | 9781568813424 1568813422 |
| Numéro OCLC : | 152581029 |
| Description : | xx, 376 p. ; 24 cm. |
| Contenu : | Preface -- Glossary of symbols -- Glossary of abbreviations -- [pt]. 1. Preliminaries -- 1. Introduction -- 1.1. Dynamical systems -- 1.2. Iterative root-finding -- 1.3. Iterative fixed-point algorithms -- 1.4. Convergence theorems -- 1.5. Positivity constraints -- 1.6. Fundamental concepts -- 2. Background -- 2.1. Iterative algorithms and their applications -- 2.2. A basic inverse problem -- 2.3. Some applications -- 2.4. The urn model for remote sensing -- 3. Basic concepts -- The geometry of Euclidean space -- 3.2. Hyperplanes in Euclidean space -- 3.3. Convex sets in Euclidean space -- 3.4. Basic linear algebra -- 3.5. Linear and nonlinear operators -- 3.6. Exercises -- 4. Metric spaces and norms -- 4.1. Metric spaces -- 4.2. Analysis in metric space -- 4.3 Norms -- 4.4. Eigenvalues and eigenvectors -- 4.5. Matrix norms -- 4.6. Exercises. [pt]. 2. Overview -- 5. Operators -- 5.1. Operators -- 5.2. Two useful identities -- 5.3. Strict contractions -- 5.4. Orthogonal projection operators -- 5.5. Averaged operators -- 5.6. Affine linear operators -- 5.7. Paracontractive operators -- 5.8. Exercises -- 6. Problems and algorithms -- 6.1. Systems of linear equations -- 6.2. Positive solutions of linear equations -- 6.3. Sensitivity to noise -- 6.4. Convex sets as constraints -- 6.5. Algorithms based on orthogonal projection -- 6.6. Steepest descent minimization -- 6.7. Bregman projections and the SGP -- 6.8. Applications -- [pt]. 3. Operators -- 7. Averaged and paracontractive operators -- 7.1. Solving linear systems of equations -- 7.2. Averaged operators -- 7.3. Paracontractive operators -- 7.4. Linear and affine paracontractions -- 7.5. Other classes of operators. [pt]. 4. Algorithms -- 8. The algebraic reconstruction technique -- 8.1. Algebraic reconstruction technique -- 8.1. The ART -- 8.2. When Ax = b has solutions-- 8.3. When ax = b has no solutions -- 8.4. Regularized ART -- 8.5. Avoiding the limit cycle -- 9. Simultaneous and block-iterative ART -- 9.1. Cimmino's algorithm -- 9.2. The Landweber algorithms -- 9.3. The block-iterative ART -- 9.4. The rescaled block-iterative ART -- 9.5. Convergence of the RBI-ART -- 9.6. Using sparseness -- 10. Jacobi and Gauss-Seidel methods -- 10.1. The Jacobi and Gauss-Seidel methods : an example -- 10.2. Splitting methods -- 10.3. Some examples of splitting methods -- 10.4. The Jacobi algorithm and JOR -- 10.5. The Gauss-Seidel method and SOR -- 11. Conjugate-direction methods in optimization -- 11.1 Iterative minimization -- 11.2. Quadratic optimization -- 11.3. Conjugate bases for R[superscript]j -- 11.4. The conjugate gradient method -- 11.5. Exercises. [pt]. 5. Positivity in linear systems -- 12. The multiplicative ART (MART) -- 12.1. A special case of MART -- 12.2. MART in the general case -- 12.3. ART and MaRT as sequential projection methods -- 12.4. Proof of convergence for MART -- 12.5. Comments on the rate of convergence of MART -- 13. Rescaled block-iterative (RBI) methods -- 13.1. Overview -- 13.2. The SMART and the EMML algorithm -- 13.3. Ordered-subset versions -- 13.4. The RBI-SMART -- 13.5. The RBI-EMML -- 13.6. RBI-SMART and entropy maximization -- [pt]. 6. Stability -- 14. Sensitivity to noise -- 14.1. Where does sensitivity come from? -- 14.2. Iterative regularization -- 14.3. A Bayesian view of reconstruction -- 14.4. The gamma prior distribution for x -- 14.5. The one-step-late alternative -- 14.6. Regularizing the SMART -- 14.7. De Pierro's surrogate-function method -- 14.8. Block-iterative regularization -- 15. Feedback in block-iterative reconstruction -- 15.1. Feedback in ART -- 15.2. Feedback in RBI methods. [pt]. 7. Optimization -- 16. Iterative optimization -- 16.1. Functions of a single real variable -- 16.2. Functions of several real variables -- 16.3. Gradient descent optimization -- 16.4. The Newton-Raphson approach -- 16.5. Rates of convergence -- 16.6. Other approaches -- 17. Convex sets and convex functions -- 17.1. Optimizing functions of a single real variable -- 17.2. Optimizing functions of several real variables -- 17.3. Convex feasibility -- 17.4. Optimization over a convex set -- 17.5. Geometry of convex sets -- 17.6. Projecting onto convex level sets -- 17.7. Projecting onto the intersection of convex sets -- 18. Generalized projections onto convex sets -- 18.1. Bregman functions and Bregman distances -- 18.2. The successive generalized projections algorithm -- 18.3. Bregman's primal-dual algorithm -- 18.4. Dykstra's algorithm for Bregman projections -- 19. The split feasibility problem -- 19.1. The CQ algorithm -- 19.2. Particular cases of the CQ algorithm -- 20. Nonsmooth optimization -- 20.1. Moreau's proximity operators -- 20.2. Forward-backward splitting-- 20.3. Proximity operators using Bregman distances -- 20.4. The interior-point algorithm (IPA) -- 20.5. Computing the iterates -- 20.6. Some examples. 21. An interior-point optimization method -- 21.1. Multiple-distance successive generalized projection -- 21.2. An interior-point algorithm (IPA) -- 21.3. The MSGP algorithm -- 21.4. An interior-point algorithm for iterative optimization -- 22. Linear and convex programming -- 22.1. Primal and dual problems -- 22.2. The simplex method -- 22.3. Convex programming -- 23. Systems of linear inequalities -- 23.1. Projection onto convex sets -- 23.2. Solving Ax = b -- 23.3. The Agmon-Motzkin-Schoenberg algorithm -- 24. Constrained iteration methods -- 24.1. Modifying the KL distance -- 24.2. The ABMART algorithm -- 24.3. The ABEMML algorithm -- 25. Fourier transform estimation -- 25.1. The limited-Fourier-data problem -- 25.2. Minimum-norm estimation -- 25.3. Fourier-transform data -- 25.4. The discrete PDFT (DPDFT). [pt]. 8. Applications -- 26. Tomography -- 26.1. X-ray transmission tomography -- 26.2. Emission tomography -- 26.3. Image reconstruction in tomography -- 27. Intensity-modulated radiation therapy -- 27.1. The extended CQ algorithm -- 27.2. Intensity-modulated radiation therapy -- 27.3. Equivalent uniform dosage functions -- 28. Magnetic-resonance imaging -- 28.1. An overview of MRI -- 28.2. Alignment -- 28.3. Slice isolation -- 28.4. Tipping -- 28.5. Imaging -- 28.6. The general formulation -- 28.7. The received signal -- 29. Hyperspectral imaging -- 29.1. Spectral component dispersion -- 29.2. A single point source -- 29.3. Multiple point sources -- 29.4. Solving the mixture problem -- 30. Planewave propagation -- 30.1. Transmission and remote sensing 30.2. The transmission problem -- 30.3. Reciprocity -- 30.4. Remote sensing -- 30.5. The wave equation -- 30.6. Planewave solutions -- 30.7. Superposition and the Fourier transform -- 30.8. Sensor arrays -- 30.9. The remote-sensing problem -- 30.10. Sampling -- 30.11. The limited-aperture problem -- 30.12. Resolution -- 30.13. Discrete data-- 30.14. The finite-data problem -- 30.15. Functions of several variables -- 30.16. Broadband signals -- 31. Inverse problems and the Laplace transform -- 31.1. The Laplace transform and the ozone layer -- 31.2. The Laplace transform and energy spectral estimation -- 32. Detection and classification -- 32.1. Estimation -- 32.2. Detection -- 32.3. Discrimination -- 32.4. Classification -- 32.5. More realistic models. [pt]. 9. Appendices -- A. Bregman-Legendre functions -- A.1. Essential smoothness and essential strict convexity -- g A.2. Bregman projections onto closed convex sets -- A.3. Bregman-Legendre functions -- A.4. Useful results about Bregman-Legendre functions -- B. Bregman-paracontractive operators -- B.1. Bregman paracontractions -- B.2. Extending the EKN theorem -- B.3. Multiple Bregman distances -- C. The Fourier transform -- C.1. Fourier-transform pairs -- C.2. The Dirac delta -- C.3. Practical limitations -- C.4. Two-dimensional Fourier transforms -- D. The EM algorithm -- D.1. The discrete case -- D.2. The continuous case -- E. Using prior knowledge in remote sensing -- E.1. The optimization approach -- E.2. Introduction to Hilbert space -- E.3. A class of inner products -- E.4. Minimum-T-norm solutions -- E.5. The case of Fourier-transform data -- F. Optimization in remote sensing -- F.1. The general form of the cost function -- F.2. The conditions -- Bibliography -- Index. |
| Responsabilité : | Charles L. Byrne. |
| Plus d’informations : |
Table des matières :
Part I. Preliminaries -- 1. Introduction -- 2. Background -- 3. Basic concepts -- 4. Metric spaces and norms -- Part II. Overview -- 5. Operators -- 6. Problems and algorithms -- Part III. Operators -- 7. Averaged and paracontractive operators -- Part IV. Algorithms -- 8. The algebraic reconstruction technique -- 9. Simultaneous and block-iterative ART -- 10. Jacobi and Gauss-Seidel methods -- 11. Conjugate-direction methods in optimization -- Part V. Positivity in linear systems -- 12. The multiplicative ART (MART) -- 13. Rescaled block-iterative (RBI) methods -- Part VI. Stability -- 14. Sensitivity to noise -- 15. Feedback in block-iterative reconstruction -- Part VII. Optimization -- 16. Iterative optimization -- 17. Convex sets and convex functions -- 18. Generalized projections onto convex sets -- 19. The split feasibility problem -- 20. Nonsmooth optimization -- 21. An interior-point optimization method -- 22. Linear and convex programming -- 23. Systems of linear inequalities -- 24. Constrained iteration methods -- 25. Fourier transform estimation -- Part VIII. Applications -- 26. Tomography -- 27. Intensity-modulated radiation therapy -- 28. Magnetic-resonance imaging -- 29. Hyperspectral imaging -- 30. Planewave propagation -- 31. Inverse problems and the Laplace transform -- 32. Detection and classification -- Part IX. Appendices -- A. Bregman-Legendre functions -- B. Bregman-paracontractive operators -- C. The Fourier transform -- D. The EM algorithm -- E. Using prior knowledge in remote sensing -- F. Optimization in remote sensing -- Bibliography.
Critiques
Synopsis de l’éditeur
" "... written for scientists and engineers, and mostly concerned with operators on finite-dimensional Euclidean space." -SciTech Book News, March 2008 With an emphasis on the technique's broad spectrum of practical applications, Charles Byrne's Applied Iterative Methods provides a thorough treatment of the iterative approach, one of the most fundamental processes used in numerical analysis. ... Unique in its cohesive treatment of a diverse array of algorithms, this book serves as a self-contained guide for those interested in exploring the many applications ofthis technique. -L'Enseignement Mathematique, August 2008 This book gives an overview of [inverse] problems and techniques for the solution of industrial inverse problems arising in acoustic signal processing, optical imaging and medical tomography. Byrne has made significant contributions to this area for some time, and many of these important results are collected in this book. The methods are analyzed on a sound mathematical functional analytical basis... The book can be used as a text for a graduate-level course on interative methods for linear systems for mathematicians, computer scientists or engineers. The presentation is very clear. -Maxim Larin, Mathematiacl Reviews, August 2008" Lire la suite...
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de julienna_lin mise à jour 2009-07-28