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| Material Type: | Internet resource |
|---|---|
| Document Type: | Book, Internet Resource |
| All Authors / Contributors: |
C L Byrne |
| ISBN: | 9781568813424 1568813422 |
| OCLC Number: | 152581029 |
| Description: | xx, 376 p. ; 24 cm. |
| Contents: | 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. |
| Responsibility: | Charles L. Byrne. |
| More information: |
Table of Contents:
by
clayton994 (WorldCat user on 2008-07-17)
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.
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