On some optimization techniques in image reconstruction from projections

Applied Numerical Mathematics

Volumn 3, Issue 5, 1987, Pages 365-391

  Censor, Yair ^a   Herman, Gabor T ^b  

^a UNIVERSITY OF HAIFA   (Israel)

^b HOSPITAL OF THE UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOMEDICAL ENGINEERING; COMPUTER PROGRAMMING - ALGORITHMS; MATHEMATICAL TECHNIQUES - NUMERICAL ANALYSIS; OPTIMIZATION;

FINITE-SERIES EXPANSION METHODS;

IMAGE PROCESSING;

EID: 0023438279     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/0168-9274(87)90028-6     Document Type: Article

References (114)

1. The relaxation method for linear inequalities
2. An interior points algorithm for the convex feasibility problem
3. Contributions to radiation therapy treatment planning
4. Seismic tomography
5. Connections between the Cimmino-method and the Kaczmarz-method for the solution of singular and regular systems of equations
6. Quadratic optimization for image reconstruction, II
7. The role of duality in optimization problems involving entropy functionals, with applications to information theory
8. The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming
9. Maximum entropy spectral analysis
10. An automatic relaxation method for solving interval linear inequalities
11. Entropy optimization via entropy projections
12. Finite series-expansion reconstruction methods
13. Intervals in linear and nonlinear problems of image reconstruction
14. Iterative methods for the convex feasibility problem
15. Row-action methods for huge and sparse systems and their applications
16. A computational solution of the inverse problem in radiation therapy treatment planning
17. Strong underrelaxation in Kaczmarz's method for inconsistent systems
18. New methods for linear inequalities
19. A method of iterative data refinement and its applications
20. Methods for entropy maximization with applications in image processing
21. Special-purpose algorithms for linearly constrained entropy maximization
22. An iterative row-action method for interval convex programming
23. Cyclic subgradient projections
24. Optimization of “log x”-entropy over linear equality constraints
25. Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing
26. Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari
27. Maximum entropy imaging: Theory and philosophy
28. Generalized iterative scaling for log linear models
29. Maximum likehood from incomplete data via the EM algorithm
30. A relaxed version of Bregman's method for convex programming
31. A simultaneous projection method for linear inequalities
32. Geometric programming Methods computations and applications
33. Iterative algorithms for large partitioned linear systems with applications to image reconstruction
34. On some methods for entropy maximization and matrix scaling
35. Fejer mappings and convex programming
36. Entropy in linear programs
37. Satellite remote sensing by the technique of computed tomography
38. Image enhancement and restoration
39. Maximum information data processing: Application to optical signals
40. Statistical models for the image restoration problem
41. Unified theory for estimating frequency-of-occurence laws and optical objects
42. Iterative methods for the three-dimensional reconstruction of an object from projections
43. The relaxation method for solving systems of linear inequalities
44. Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography
45. The method of projections for finding the common point of convex sets
46. Least-squares solution of linear inequalities
47. Application of maximum entropy and Bayesian optimization methods to image reconstruction from projections
48. Image Reconstruction from Projections: Implementation and Applications
49. Mathematical optimization versus practical performance A case study based on the maximum entropy criterion in image reconstruction
50. A relaxation method for reconstructing objects from noisy X-rays
51. Comments on a statistical model for positron emission tomography
52. A family of iterative quadratic optimization algorithms for pairs of inequalities with application in diagnostic radiology
53. Iterative reconstruction algorithms
54. Quadratic optimization for image reconstruction, I
55. Iterative relaxation methods for image reconstruction
56. Multilevel image reconstruction
57. A quadratic programming procedure
58. Erratum
59. An introduction to NMR imaging: From the Bloch equation to the imaging equation
60. Two dimensional spectral estimation
61. On the rationale of maximum-entropy methods
62. Which is the better entropy expression for speech processing: - S log S or log S?
63. An improved algorithm for reprojecting rays through pixel images
64. Angenäherte Auflösung von Systemen linearer Gleichungen
65. Twenty-five years of maximum-entropy principle
66. Telefoonverkeersrekening
67. Properties of Kruithof's projection method
68. Bregman's balancing method
69. EM reconstruction algorithms for emission and transmission tomography
70. A convergent algorithm for maximum entropy image restoration with a medical X-ray application
71. Extensions of Hildreth's row-action method for quadratic programming
72. Reconstruction algorithms: Transform methods
73. Mathematical problems of computerized tomography
74. Convergence of the cyclical relaxation method for linear inequalities
75. On the convergence of the discrete ART algorithm for the reconstruction of digital pictures from their projections
76. The method of Kaczmarz and row orthogonalization for solving linear equations and least squares problems in Hilberts spaces
77. Solution of underdetermined nonlinear equations by stationary iteration methods
78. MENT: A maximum entropy algorithm for reconstructing a source from projection data
79. The relaxation method for linear inequalities
80. Continuous and semicontinuous analogues of iterative methods of Cimmino and Kaczmarz with applications to the inverse Radon transform
81. Iterative reconstruction algorithms Convergence as a function of spatial frequency
82. Symmetric duality and a convergent subgradient method for discrete, linear, constrained approximation problems with arbitrary norms appearing in the o bjective function and in the constraints
83. Lösung linearer Gleichungssysteme durch Projektion auf Schnitträume von Hyperebenen und Berechnung einer verallgemeinerten Inversen
84. Decomposition through formalization in a product space
85. Uber die Bestimmung von Funktionen durch ihre Integralwerte langs gewisser Mannigfaltigkeiten
86. Recent developments in the industrial application of computerized tomography with ionizing radiation
87. A maximum likelihood approach to emission image reconstruction from projections
88. Maximum likelihood reconstruction in positron emission tomography
89. Practical and mathematical aspects of the problem of reconstructing objects from radiographs
90. The x-ray transform
91. Partial inverse of a monotone operator
92. The defect correction principle and discretization methods
93. Projection method for solving a singular system of linear equations and its applications
94. A note of the ART of relaxation
95. Reconstructing pictures from projections: on the convergence of the ART algorithm with relaxation
96. SMART—an algorithm for reconstructing pictures from projections
97. A statistical model for positron emission tomography
98. Reply to Herman, Censor, Gordon and Lewitt
99. Maximum entropy techniques for digital image reconstruction
100. Maximum likelihood, entropy maximization, and the geometric programming approaches to the calibration of trip distribution models