Convergent block-iterative algorithms for image reconstruction from inconsistent data

IEEE Transactions on Image Processing

Volumn 6, Issue 9, 1997, Pages 1296-1304

  Byrne, Charles L ^a,b  

^a IEEE   (United States)

^b UNIVERSITY OF MASSACHUSETTS LOWELL   (United States)

Author keywords

Restoration; Tomography

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; FEEDBACK; ITERATIVE METHODS; SET THEORY; VECTORS;

LIMIT CYCLE (LC) VECTORS; SIMULTANEOUS MULTIPLICATIVE ALGEBRAIC RECONSTRUCTION TECHNIQUE;

IMAGE RECONSTRUCTION;

EID: 0031233862     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/83.623192     Document Type: Article

References (25)

1. C. Byrne, "Block-iterative methods for image reconstruction from projections," IEEE Trans. Image Processing, vol. 5, pp. 792-794, May 1996.
2. G. Herman and L. Meyer, "Algebraic reconstruction techniques can be made computationally efficient," IEEE Trans. Med. Imag., vol. 12, pp. 600-609, Sept. 1993.
3. H. Guan and R. Gordon, "A projection access order for speedy convergence of ART (algebraic reconstruction technique): A multilevel scheme for computed tomography," Phys. Med. Biol., vol. 39, pp. 2005-2022, 1994.
4. R. Gordon, R. Bender, and G. Herman, "Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography," J. Theoret. Biol., vol. 29, pp. 471-481, 1970.
5. K. Tanabe, "Projection method for solving a singular system of linear equations and its applications," Numer. Math., vol. 17, pp. 203-214, 1971.
6. M. Trammer, "SMART - An algorithm for reconstructing pictures from projections," J. Appl. Math. Phys., vol. 34, pp. 746-753, Sept. 1983.
7. C. Byrne, "Iterative image reconstruction algorithms based on cross-entropy minimization," IEEE Trans. Image Processing, vol. 2, pp. 96-103, Jan. 1993.
8. _, "Erratum and addendum to 'Iterative image reconstruction algorithms based on cross-entropy minimization,'" IEEE Trans. Image Processing, vol. 4, pp. 225-226, Feb. 1995.
9. _, "Iterative reconstruction algorithms based on cross-entropy minimization," in Image Models (and Their Speech Model Cousins), vol. 80, S. Levinson and L. Shepp, Eds. New York: Springer-Verlag, 1996.
10. _, "Accelerating the EMML algorithm and related iterative algorithms by rescaled block-iterative (RBI) methods," IEEE Trans. Image Processing, to be published.
11. S. Kaczmarz, "Angenaeherte Aufloesung von Systemen linearen Gleichungen," Bull. Acad. Polen. Sci. Lett., vol. A35, pp. 355-357, 1937.
12. G. Herman, A. Lent, and P. Lutz, "Relaxation methods for image reconstruction," Commun. Assoc. Comput. Mach., vol. 21, pp. 152-158, 1978.
13. M. Trummer, "Reconstructing pictures from projections: On the convergence of the ART algorithm with relaxation," Computing, vol. 26, pp. 189-195, 1981.
14. P. Eggermont, G. Herman, and A. Lent, "Iterative algorithms for large partitioned linear systems, with applications to image reconstruction," Linear Algebra Appl., vol. 40, pp. 37-67, 1981.
15. A. Dax, "The convergence of linear stationary iterative processes for solving singular unstructured systems of linear equations," SIAM Rev., vol. 32, pp. 611-635, Dec. 1990.
16. Y. Censor, P. Eggermont, and D. Gordon, "Strong underrelaxation in Kaczmarz's method for inconsistent systems," Numer. Math., vol. 41, pp. 83-92, 1983.
17. S. Kullback and R. Leibler, "On information and sufficiency," Ann. Math. Stat., vol. 22, pp. 79-86, 1951.
18. A. Lent, "A convergent algorithm for maximum entropy image restoration with a medical x-ray application," in Image Analysis and Evaluation, R. Shaw, Ed. Washington, DC: SPSE, 1977, pp. 238-243.
19. A. R. DePierro and A. N. Iusem, "A relaxed version of Bregman's method for convex programming," J. Optimiz. Theory Appl., vol. 51, pp. 421-440, 1986.
20. Y. Censor, "Finite series-expansion reconstruction methods," Proc. IEEE, vol. 71, pp. 409-419, Mar. 1983.
21. G. Herman, "Applications of maximum entropy and Bayesian optimization methods to image reconstruction from projections," in C. P. Smith and W. T. Grandy, Jr., Eds., Maximum Entropy and Bayesian Methods in Inverse Problems. D. Reidel, 1985., pp. 319-338.
22. C. P. Smith and W. T. Grandy, Jr., Eds., Maximum Entropy and Bayesian Methods in Inverse Problems. D. Reidel, 1985.
23. H. Hudson and R. Larkin, "Accelerated image reconstruction using ordered subsets of projection data," IEEE Trans. Med. Imag. vol. 13, pp. 601-609, Dec. 1994.
24. W. Xuan, "Evaluating a feedback technique in image reconstruction from projections," Tech. Rep., Dept. Statist., MacQuarie Univ., Sydney, Australia, Dec. 1993.
25. J. Browne and A. DePierro, "A row-action alternative to the EM algorithm for maximizing likelihoods in emission tomography," IEEE Trans. Med. Imag., vol. 15, pp. 687-699, Oct. 1996.