Combining ordered subsets and momentum for accelerated X-ray CT image reconstruction

IEEE Transactions on Medical Imaging

Volumn 34, Issue 1, 2015, Pages 167-178

  Kim, Donghwan ^a   Ramani, Sathish ^b   Fessler, Jeffrey A ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

^b GE GLOBAL RESEARCH   (United States)

Author keywords

Computed tomography (CT); momentum; ordered subsets; parallelizable iterative algorithms; relaxation; separable quadratic surrogates; statistical image reconstruction; stochastic gradient

Indexed keywords

ALGORITHMS; COMPUTER ARCHITECTURE; IMAGE PROCESSING; IMAGE RECONSTRUCTION; ITERATIVE METHODS; MOMENTUM; SET THEORY; SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY; STOCHASTIC SYSTEMS; TOMOGRAPHY;

ITERATIVE ALGORITHM; ORDERED SUBSETS; RELAXATION; SEPARABLE QUADRATIC SURROGATES; STATISTICAL IMAGE RECONSTRUCTION; STOCHASTIC GRADIENT;

COMPUTERIZED TOMOGRAPHY;

ACCELERATION; ALGORITHM; ARTICLE; COMPUTER ASSISTED TOMOGRAPHY; GEOMETRY; HUMAN; IMAGE QUALITY; IMAGE RECONSTRUCTION; ITERATIVE ALGORITHM; METHODOLOGY; SHOULDER; STATISTICAL ANALYSIS; X RAY; IMAGE PROCESSING; PROCEDURES; THORAX RADIOGRAPHY;

ALGORITHMS; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; PHANTOMS, IMAGING; RADIOGRAPHY, THORACIC; TOMOGRAPHY, X-RAY COMPUTED;

EID: 84928888532     PISSN: 02780062     EISSN: 1558254X     Source Type: Journal    
DOI: 10.1109/TMI.2014.2350962     Document Type: Article

References (56)

1. J. A. Fessler, M. Sonka and J. M. Fitzpatrick, Eds., "Statistical image reconstruction methods for transmission tomography," in Handbook of Medical Imaging, Volume 2. Medical Image Processing and Analysis. Bellingham: SPIE, 2000, pp. 1-70.
2. I. A. Elbakri and J. A. Fessler, "Statistical image reconstruction for polyenergetic X-ray computed tomography," IEEE Trans. Med. Imag., vol. 21, no. 2, pp. 89-99, Feb. 2002.
3. K. Sauer and C. Bouman, "A local update strategy for iterative reconstruction from projections," IEEE Trans. Signal Process., vol. 41, no. 2, pp. 534-548, Feb. 1993.
4. J.-B. Thibault, K. Sauer, C. Bouman, and J. Hsieh, "A three-dimensional statistical approach to improved image quality for multi-slice helical CT," Med. Phys., vol. 34, no. 11, pp. 4526-4544, Nov. 2007.
5. J. A. Fessler, E. P. Ficaro, N. H. Clinthorne, and K. Lange, "Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction," IEEE Trans. Med. Imag., vol. 16, no. 2, pp. 166-175, Apr. 1997.
6. Z. Yu, J.-B. Thibault, C. A. Bouman, K. D. Sauer, and J. Hsieh, "Fast model-based X-ray CT reconstruction using spatially non-homogeneous ICD optimization," IEEE Trans. Image Process., vol. 20, no. 1, pp. 161-175, Jan. 2011.
7. J. A. Fessler and S. D. Booth, "Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction," IEEE Trans. Image Process., vol. 8, no. 5, pp. 688-699, May 1999.
8. H. M. Hudson and R. S. Larkin, "Accelerated image reconstruction using ordered subsets of projection data," IEEE Trans. Med. Imag., vol. 13, no. 4, pp. 601-609, Dec. 1994.
9. H. Erdoʇan and J. A. Fessler, "Ordered subsets algorithms for transmission tomography," Phys. Med. Biol., vol. 44, no. 11, pp. 2835-2851, Nov. 1999.
10. T. Goldstein and S. Osher, "The split Bregman method for L1-regular-ized problems," SIAM J. Imag. Sci., vol. 2, no. 2, pp. 323-343, 2009.
11. S. Ramani and J. A. Fessler, "A splitting-based iterative algorithm for accelerated statistical X-ray CT reconstruction," IEEE Trans. Med. Imag., vol. 31, no. 3, pp. 677-688, Mar. 2012.
12. M. G. McGaffin, S. Ramani, and J. A. Fessler, "Reduced memory augmented Lagrangian algorithm for 3D iterative X-ray CT image reconstruction," in Proc. SPIE 8313 Med. Imag. Phys. Med. Imag., 2012, p. 831327.
13. D. P. Bertsekas, "Multiplier methods: A survey," Automatica, vol. 12, no. 2, pp. 133-145, Mar. 1976.
14. A. Chambolle and T. Pock, "A first-order primal-dual algorithm for convex problems with applications to imaging," J. Math. Imag. Vision, vol. 40, no. 1, pp. 120-145, 2011.
15. E. Y. Sidky, J. H. Jorgensen, and X. Pan, "Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm," Phys. Med. Biol., vol. 57, no. 10, pp. 3065-3092, May 2012.
16. E. Y. Sidky, J. S. Jrgensen, and X. Pan, "First-order convex feasibility algorithms for X-ray CT," Med. Phys., vol. 40, no. 3, p. 031115, 2013.
17. Y. Nesterov, "A method for unconstrained convex minimization problem with the rate of convergence," Dokl. Akad. Nauk. USSR, vol. 269, no. 3, pp. 543-547, 1983.
18. Y. Nesterov, "Smooth minimization of non-smooth functions," Math. Program., vol. 103, no. 1, pp. 127-152, May 2005.
19. A. Beck and M. Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM J. Imag. Sci., vol. 2, no. 1, pp. 183-202, 2009.
20. K. Choi, J. Wang, L. Zhu, T.-S. Suh, S. Boyd, and L. Xing, "Compressed sensing based cone-beam computed tomography reconstruction with a first-order method," Med. Phys., vol. 37, no. 9, pp. 5113-5125, Nov. 2010.
21. T. L. Jensen, J. H. Jrgensen, P. C. Hansen, and S. H. Jense, "Implementation of an optimal first-order method for strongly convex total variation regularization," BIT Numer. Math., vol. 52, no. 2, pp. 329-356, Jun. 2012.
22. S. Anthoine, J.-F. Aujol, Y. Boursier, and C. Mélot, "Some proximal methods for Poisson intensity CBCT and PET," Inverse Prob. Imag., vol. 6, no. 4, pp. 565-598, Nov. 2012.
23. Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course. New York: Kluwer, 2004.
24. Y. Nesterov, "Gradient methods for minimizing composite functions," Math. Program., vol. 140, no. 1, pp. 125-161, Aug. 2013.
25. A. Beck and M. Teboulle, "Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems," IEEE Trans. Image Process., vol. 18, no. 11, pp. 2419-2434, Nov. 2009.
26. D. Kim, S. Ramani, and J. A. Fessler, "Ordered subsets with momentum for accelerated X-ray CT image reconstruction," in Proc. IEEE Conf. Acoust. Speech Signal Process., 2013, pp. 920-923.
27. D. Kim, S. Ramani, and J. A. Fessler, "Accelerating X-ray CT ordered subsets image reconstruction with Nesterov's first-order methods," in Proc. Int. Mtg. on Fully 3D Image Recogn. in Rad. and Nucl. Med., 2013, pp. 22-25.
28. S. Ahn, J. A. Fessler, D. Blatt, and A. O. Hero, "Convergent incremental optimization transfer algorithms: Application to tomography," IEEE Trans. Med. Imag., vol. 25, no. 3, pp. 283-296, Mar. 2006.
29. D. Kim, D. Pal, J.-B. Thibault, and J. A. Fessler, "Accelerating ordered subsets image reconstruction for X-ray CT using spatially non-uniform optimization transfer," IEEE Trans. Med. Imag., vol. 32, no. 11, pp. 1965-1978, Nov. 2013.
30. O. L. Mangasarian and M. V. Solodov, "Serial and parallel backprop-agation convergence via nonmonotone perturbed minimization," Op-timiz. Methods Software, vol. 4, no. 2, pp. 103-116, 1994.
31. P. Tseng, "An incremental gradient(-projection) method with momentum term and adaptive stepsize rule," SIAM J. Optim., vol. 8, no. 2, pp. 506-531, 1998.
32. D. Blatt, A. O. Hero, and H. Gauchman, "A convergent incremental gradient method with a constant step size," SIAM J. Optim., vol. 18, no. 1, pp. 29-51, 2007.
33. O. Devolder, Stochastic First Order Methods in Smooth Convex Optimization CORE, Catholic Univ. Louvain, Louvain-la-Neuve, Belgium, Tech. Rep., 2011.
34. B. De Man and S. Basu, "Distance-driven projection and backpro-jection in three dimensions," Phys. Med. Biol., vol. 49, no. 11, pp. 2463-2475, Jun. 2004.
35. Y. Long, J. A. Fessler, and J. M. Balter, "3D forward and back-projection for X-ray CT using separable footprints," IEEE Trans. Med. Imag., vol. 29, no. 11, pp. 1839-1850, Nov. 2010.
36. R. C. Fair, "On the robust estimation of econometric models," Ann. Econ. Social Measure., vol. 2, pp. 667-677, Oct. 1974.
37. J. A. Fessler and W. L. Rogers, "Spatial resolution properties of pe-nalized-likelihood image reconstruction methods: Space-invariant tomographs," IEEE Trans. Image Process., vol. 5, no. 9, pp. 1346-1358, Sep. 1996.
38. A. H. Delaney and Y. Bresler, "Globally convergent edge-preserving regularized reconstruction: An application to limited-angle tomography," IEEE Trans. Image Process., vol. 7, no. 2, pp. 204-221, Feb. 1998.
39. K. Lange, D. R. Hunter, and I. Yang, "Optimization transfer using surrogate objective functions," J. Computat. Graph. Stat., vol. 9, no. 1, pp. 1-20, Mar. 2000.
40. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables. New York: Academic, 1970.
41. H. Erdoʇan and J. A. Fessler, "Monotonic algorithms for transmission tomography," IEEE Trans. Med. Imag., vol. 18, no. 9, pp. 801-814, Sep. 1999.
42. J. H. Cho and J. A. Fessler, "Accelerating ordered-subsets image reconstruction for X-ray CT using double surrogates," in Proc. SPIE 8313 Med. Imag.: Phys. Med. Imag., 2012, p. 83131X.
43. Z. Q. Luo, "On the convergence of the LMS algorithm with adaptive learning rate for linear feedforward networks," Neural Computat., vol. 32, no. 2, pp. 226-245, Jun. 1991.
44. S. Ahn and J. A. Fessler, "Globally convergent image reconstruction for emission tomography using relaxed ordered subsets algorithms," IEEE Trans. Med. Imag., vol. 22, no. 5, pp. 613-626, May 2003.
45. Y. Nesterov, "On an approach to the construction of optimal methods of minimization of smooth convex functions," Èkonom. I. Mat. Metody, vol. 24, pp. 509-517, 1988.
46. P. Tseng, On Accelerated Proximal Gradient Methods for Convex-Concave Optimization 2008 [Online]. Available: http://pages.cs.wisc. edu/~brecht/cs726docs/Tseng.APG.pdf
47. O. Devolder, F. Glineur, and Y. Nesterov, "Intermediate gradient methods for smooth convex problems with inexact oracle," 2013, CORE discussion paper 2013/17.
48. D. Kim and J. A. Fessler, "Ordered subsets acceleration using relaxed momentum for X-ray CT image reconstruction," in Proc. IEEE Nuc. Sci. Symp. Med. Im. Conf., 2013, pp. 1-5.
49. A. Nemirovski and D. Yudin, Problem Complexity and Method Efficiency in Optimization. New York: Wiley, 1983.
50. J. A. Fessler, Matlab Tomography Toolbox 2004 [Online]. Available: web.eecs.umich.edu/~fessler
51. W. P. Segars, M. Mahesh, T. J. Beck, E. C. Frey, and B. M. W. Tsui, "Realistic CT simulation using the 4D XCAT phantom," Med. Phys., vol. 35, no. 8, pp. 3800-3808, Aug. 2008.
52. F. Noo, M. Defrise, and R. Clackdoyle, "Single-slice rebinning method for helical cone-beam CT," Phys. Med. Biol., vol. 44, no. 2, pp. 561-570, Feb. 1999.
53. G. T. Herman and L. B. Meyer, "Algebraic reconstruction techniques can be made computationally efficient," IEEE Trans. Med. Imag., vol. 12, no. 3, pp. 600-609, Sep. 1993.
54. S. Ramani and J. A. Fessler, "Accelerated nonCartesian SENSE reconstruction using a majorize-minimize algorithm combining variablesplitting," in Proc. IEEE Int. Symp. Biomed. Imag., 2013, pp. 704-707.
55. M. Muckley, D. C. Noll, and J. A. Fessler, "Accelerating SENSE-type MR image reconstruction algorithms with incremental gradients," in Proc. Int. Soc. Mag. Res. Med., 2014, p. 4400.
56. B. O'Donoghue and E. Candès, "Adaptive restart for accelerated gradient schemes," Found. Computat. Math., 2014.