Multilevel image reconstruction with natural pixels

SIAM Journal on Scientific Computing

Volumn 17, Issue 1, 1996, Pages 193-216

  Henson, Van Emden ^a   Limber, Mark A ^b   Mccormick, Stephen F ^c   Robinson, Bruce T ^d  

^a NAVAL POSTGRADUATE SCHOOL   (United States)

^b Auto trol Technology Corporation   (United States)

^c UNIVERSITY OF COLORADO   (United States)

^d Accurate Information Systems   (United States)

Author keywords

Multigrid; Radon transform; Tomography

Indexed keywords

EID: 0001629702     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/0917014     Document Type: Article

References (25)

1. M. H. BOUNOCORE, W. R. BRODY, AND A. MACOVSKI, A natural pixel decomposition for two dimensional image reconstruction, IEEE Trans. Biomed. Engrg., BME-28 (1981), pp. 69-78.
2. A. BRANDT, Multi-level adaptive techniques (MLAT) for partial differential equations: Ideas and software, in Proceedings of the Symposium on Mathematical Software, 1977, Academic Press, New York, 1977, pp. 277-318.
3. _, Multi-level adaptive solutions to boundary value problems, Math. Comp., 31 (1987), pp. 333-390.
4. _, Rigorous local mode analysis of multigrid, in Preliminary Proceedings of the Fourth Copper Mountain Conference on Multigrid Methods, J. Mandel and S. F. McCormick, eds., 1989.
5. W.L. BRIGGS, A Multigrid Tutorial, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1987.
6. K. J. CAVANAUGH AND V. E. HENSON, A multilevel cost-space approach to solving the balanced long transportation problem, in Proceedings of the 6th Copper Mountain Conference on Multigrid Methods, Vol. CP-3224, NASA Conference Publications, 1993.
7. C. C. DOUGLAS AND J. DOUGLAS, A unified convergence theory for abstract multigrid or multilevel algorithms, serial and parallel, SIAM J. Numer. Anal., 30 (1993), pp. 136-158.
8. V. E. HENSON, M. A. LIMBER, S. F. MCCORMICK, AND B. T. ROBINSON, Multilevel projection methods for spotlight computed tomography, in preparation.
9. G. T. HERMAN, Image Reconstruction from Projections, Academic Press, Orlando, FL, 1980.
10. M. A. LIMBER, T. A. MANTEUFFEL, S. F. MCCORMICK, AND D. S. SHOLL, Optimal resolution in maximum entropy image reconstruction from projections with multigrid acceleration, in Proceedings of the Sixth Annual Copper Mountain Conference on Multigrid Methods, 1993.
11. A. K. LOUIS, Medical imaging: The state of the art and future development, Inverse Problems, 8 (1992), pp. 709-738.
12. J. MANDEL AND S. F. MCCORMICK, Iterative solution of elliptic equations with refinement: The model multilevel case, in Domain Decomposition Methods, T. F. Chan, ed., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1987, pp. 81-92.
13. S. F. MCCORMICK, The methods of Kaczmarz and row orthogonalization for solving linear equations and least squares problems in Hilbert space, Indiana Univ. Math. J., 26 (1977), pp. 1137-1150.
14. _, Multilevel Adaptive Methods for Partial Differential Equations, Frontiers in Applied Mathematics, Vol. 6, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1989.
15. _, Multilevel Projection Methods for Partial Differential Equations, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 62, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.
16. S. F. MCCORMICK AND J. THOMAS, The fast adaptive composite grid method (FAC) for elliptic boundary value problems, Math. Comp., 46 (1986), pp. 439-456.
17. S. F. MCCORMICK AND J. G. WADE, Multilevel parameter estimation, in Proceedings of the 5th Copper Mountain Conference on Multigrid Methods, 1991.
18. F. NATTERER, The Mathematics of Computerized Tomography, John Wiley and Sons, New York, 1986.
19. T.-S. PAN, A. E. YAGLE, N. H. CLINTHORNE, AND W. L. ROGERS, Acceleration and filtering in the generalized Landweber iteration using a variable shaping matrix, IEEE Trans. Medical Imaging, 12 (1993), pp. 278-286.
20. B. T. ROBINSON, A Multilevel Approach to the Algebraic Image Reconstruction Problem, Ph.D. thesis, Naval Postgraduate School, Monterey, CA, 1994.
21. U. RÜDE, Mathematical and Computational Techniques for Multilevel Adaptive Methods, Frontiers in Applied Mathematics, Vol. 13, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1993.
22. J. RUGE AND K. STÜBEN, Algebraic multigrid (AMG), in Multigrid Methods, S. F. McCormick, ed., Frontiers in Applied Mathematics, Vol. 3, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1987, pp. 131-177.
23. L. A. SHEPP AND B. F. LOGAN, The Fourier reconstruction of a head section, IEEE Trans. Nucl. Sci., NS-21 (1974), pp. 21-43.
24. H. STARK, J. W. WOODS, I. PAUL, AND R. HINGORANI, Direct Fourier reconstruction in computer tomography, IEEE Trans. Acoust., Speech Signal Process., ASSP-29 (1981), pp. 237-244.
25. K. TANABE, Projection method for solving a singular system of linear equations and its applications, Numer. Math., 17 (1971), pp. 203-214.