Reconstruction of three-dimensional localized objects from limited angle x-ray projections: An approach based on sparsity and multigrid image representation

Journal of Electronic Imaging

Volumn 17, Issue 3, 2008, Pages

  Soussen, Charles ^a   Idier, Jérôme ^b  

^a CENTRE DE RECHERCHE EN AUTOMATIQUE DE NANCY   (France)

^b INSTITUT DE RECHERCHE EN COMMUNICATIONS ET CYBERNÉTIQUE DE NANTES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

COARSE-TO-FINE; COMPUTED TOMOGRAPHY; CONE-BEAM PROJECTION; IMAGE PARAMETERS; IMAGE REPRESENTATIONS; INITIAL SOLUTION; MAXIMUM A POSTERIORI ESTIMATOR; MEMORY STORAGE; MULTI-GRID; MULTIGRID METHODS; RESOLUTION LEVEL; SIMULATED DATA; SYNTHETIC IMAGES; THREE-DIMENSIONAL IMAGE RECONSTRUCTION; X-RAY PROJECTIONS;

COMPUTERIZED TOMOGRAPHY; CONSTRAINED OPTIMIZATION; IMAGE RECONSTRUCTION; OBJECT RECOGNITION; PARAMETER ESTIMATION; REPAIR; SET THEORY;

THREE DIMENSIONAL;

EID: 70350675394     PISSN: 10179909     EISSN: 1560229X     Source Type: Journal    
DOI: 10.1117/1.2954960     Document Type: Article

References (51)

1. R. Zorgati, B. Duchêne, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, part I: Qualitative imaging via diffraction tomography techniques," IEEE Trans. Magn. 27(6), 4416-4437 (1991).
2. A. B. Frakt, W. C. Karl, and A. S. Willsky, "A multiscale hypothesis testing approach to anomaly detection, and localization from noisy tomographic data," IEEE Trans. Image Process. 7(6), 825-837 (1998).
3. L. Chatellier, L. Fournier, B. Charbonnier, L. Robillard, and B. Chassignole, "Characterization improvement through signal processing. Application to radiography inspection: 3D reconstruction," ASME Pressure Vessels and Piping Div. Conf., Denver, (2005).
4. I. T. Rekanos and T. D. Tsiboukis, "An inverse scattering technique for microwave imaging of binary objects," IEEE Trans. Microwave Theory Tech. 50(5), 1439-1441 (2002).
5. F. Retraint, F. Peyrin, and J.-M. Dinten, "Three-dimensional regularized binary image reconstruction, from three two-dimensional projections using a randomized ICM algorithm," Int. J. Imaging Syst. Technol. 9(2-3), 135-146 (1998).
6. C. A. Bouman and K. D. Sauer, "Nonlinear multigrid methods of optimization in Bayesian tomographic image reconstruction," Proc. SPIE 1766, 296-306 (1992).
7. B. Chalmond, F. Coldefy, and B. Lavayssière, "Tomographic reconstruction from non-calibrated noisy projections in non-destructive evaluation," Inverse Probl. 15, 399-411 (1999).
8. N. Robert, F. Peyrin, and M. J. Yaffe, "Binary vascular reconstruction from a limited, number of cone beam projections," Med. Phys. 21.(12), 1839-1851 (1994).
9. M. Allain and J. Idier, "Efficient binary reconstruction for nondestructive evaluation using gammagraphy," Inverse Probl. 23(4), 1371-1393 (2007).
10. J. A. Case, T-S. Pan, M. A. King, D.-S. Luo, B. C. Penney, and M. S. Z. Rabin, "Reduction of truncation artifacts in fan beam transmission imaging using a spatially varying Gamma prior," IEEE Trans. Nucl. Sci. 42(6), 2260-2265 (1995).
11. I.-T. Hsiao, A. Rangarajan, and G. Gindi, "Bayesian reconstruction for transmission tomography using deterministic annealing," J. Electron. Imaging 2(1), 7-16 (2003).
12. S. Gautier, J. Idler, A. Mohammad-Djafari, and B. Lavayssière, "Xray and ultrasound data fusion," Proc. IEEE ICIP, Chicago, pp. 366-369 (1998).
13. K. D. Sauer and C. A. Bouman, "A local update strategy for iterative reconstruction from projections," IEEE Trans. Signal Peocess. 41(2), 534-548 (1993).
14. S. Brette and J. Idler, "Optimized single site update algorithms for image deblurring," Proc. IEEE ICIP, Lausanne, pp. 65-68 (1996).
15. N. Villain, Y. Goussard, J. Idier, and M. Allain, "Three-dimensional edge-preserving image enhancement for computed tomography," IEEE Trans. Med. Imaging 22(10), 1275-1287 (2003).
16. Y. Bresler and A. Macovski, "Three-dimensional reconstruction from projections with incomplete and noisy data by object estimation," IEEE Trans. Acoust., Speech, Signal Process. ASSP-35(8), 1139-1152 (1987).
17. P. Milanfar, W. C. Karl, and A. S. Willsky, "Reconstructing binary polygonal objects from projections: A statistical view," Comput. Vis. Graph. Image Process. 56(5), 371-391 (1994).
18. K. M. Hanson, R. L. Bilisoly, and G. S. Cunningham, "Kinky tomographic reconstruction," Proc. SPIE 2710, 156-166 (1996).
19. X. L. Battle, C. Le Rest, A. Turzo, and Y. J. Bizais, "3D attenuation map reconstruction using geometrical models and free-form deformations," IEEE Trans. Med. Imaging 19(5), 404-411 (2000).
20. C. Soussen and A. Mohammad-Djafari, "Polygonal and polyhedral contour reconstruction in computed tomography," IEEE Trans. Image Process. 13(11), 1507-1523 (2004).
21. F. Santosa, "A level-set approach for inverse problems involving obstacles," ESAIM: COCV, 1, 17-33 (1996).
22. D. F. Yu and J. A. Fessier, "Edge-preserving tomographic reconstruction, with nonlocal regularization," IEEE Trans. Med. Imaging 21(2), 159-173 (2002).
23. H. Feng, W. C. Karl, and D. A. Castanon, "A curve evolution approach to object-based tomographic reconstruction," IEEE Trans. Image Process. 12(1), 44-57 (2003).
24. J. G. Brankov, Y. Yang, and M. N. Wernick, "Tomographic image reconstruction based on content-adaptive mesh model," IEEE Trans. Med. Imaging 23(2), 202-212 (2004).
25. L. Fillatre and I. Nikiforov, "Non-Bayesian detection, and detectability of anomalies from a few noisy tomographic projections," IEEE Trans. Signal Process. 55(2), 401-413 (2007).
26. T. Olson, and J. DeStefano, "Wavelet localization of the Radon transform," IEEE Trans. Signal Process. 42(8), 2055-2067 (1994).
27. A. H. Delaney and Y. Bresler, "Multiresolution tomographic reconstruction using wavelets," IEEE Trans. Image Process. 4(6), 799-813 (1995).
28. F. Rashid-Farrokhi, K. J. Ray Liu, C. A. Berenstein, and D. Walnut, "Wavelet-based multiresolution local tomography," IEEE Trans. Image Process. 6(10), 1412-1430 (1997).
29. S. Bonnet, F. Peyrin, F. Turjman, and R. Prost, "Multiresolution reconstruction in fan-beam tomography," IEEE Trans. Image Process. 11(3), 169-176 (2002).
30. M. V. Ranganath, A. P. Dhawan, and N. Mullani, "A multigrid expectation maximization reconstruction algorithm for positron emission, tomography," IEEE Trans. Med. Imaging 7(4), 273-278 (1988).
31. T.-S. Pan and A. E. Yagle, "Numerical study of multigrid implementations of some iterative image reconstruction algorithms," IEEE Trans. Med. Imaging 10(4), 572-588 (1991).
32. W. Zhu, Y. Wang, Y. Deng, Y. Yao, and R. L. Barbour, "A waveletbased multiresolution regularized least squares reconstruction approach for optical tomography," IEEE Trans. Med. Imaging 16(2), 210-217 (1997).
33. J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, "Nonlinear multigrid algorithms for Bayesian optical diffusion tomography," IEEE Trans. Image Process. 10(6), 909-922 (2001).
34. S. Oh, A. B. Milstein, C. A. Bouman, and K. J. Webb, "A general framework, for nonlinear multigrid inversion," IEEE Trans. Image Process. 14(1), 125-140 (2005).
35. S. S. Saquib, C. A. Bouman, and K. D. Sauer, "A non-homogeneous MRF model for multiresolution Bayesian estimation," Proc. IEEE ICIP, Vol. 2, Lausanne, pp. 445-448 (1996).
36. T. Frese, C. A. Bouman, and K. D. Sauer, "Adaptive wavelet graph model for Bayesian tomographic reconstructions," IEEE Trans. Image Process. 11(7), 756-770 (2002).
37. K. Sauer and J.-B. Thibault, "Imaging from low-intensity data," in Bayesian Approach to Inverse Problems, J. Idier, Ed. pp. 357-374, ISTE Ltd. and Wiley, Hoboken, NJ (2008).
38. C. A. Bouman and K. D. Sauer, "A unified approach to statistical tomography using coordinate descent optimization," IEEE Trans. Image Process. 5(3), 480-492 (1996).
39. J. A. Fessier, "Penalized weighted least-squares image reconstruction for positron emission tomography," IEEE Trans. Med. Imaging 13(2), 290-300 (1994).
40. M. E. Davison, "The ill-conditioned nature of the limited angle tomography problem," SIAM J. Appl. Math, 43(2), 428-448 (1983).
41. M. Nikolova and M. K. Ng, "Analysis of half-quadratic minimization methods for signal, and image recovery," SIAM J. Sci. Comput. (USA) 27(3), 937-966 (2005).
42. C. Soussen and J. Idier, "3D reconstruction of localized objects from radiographs and based on multiresolution and sparsity," in Proc. IEEE ICIP, Vol. III, Genova, Italy, pp. 744-747 (2005).
43. D. P. Bertsekas, Nonlinear Programming, 2 ed., Athena Scientific, Belmont, MA, (1999).
44. D. Geman and G. Reynolds, "Constrained restoration and the recovery of discontinuities," IEEE Trans. Pattern Anal. Mack Intell. 14(3), 367-383 (1992).
45. J. Idier, "Convex half-quadratic criteria and interacting auxiliary variables for image restoration," IEEE Trans. Image Process. 10(7), 1001-1009 (2001).
46. R. T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, NJ (1970).
47. J. Arvo, Graphics Gems II, Academic Press, New York (1991).
48. C. A. Johnson, J. Seidel, and A. Sofer, "Interior-point methodology for 3-D PET reconstruction," IEEE Trans. Med. Imaging 19(4), 271-285 (2000).
49. M. R. Osborne, B. Presnell, and B. A. Turlach, "A new approach to variable selection in least squares problems," IMA J. Numer. Anal. 20(3), 389-403 (2000).
50. B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, "Least angle regression," Ann. Stat. 32(2), 407-451 (2004).
51. S. Rosset and J. Zhu, "Discussion of 'Least angle regression' by B. Efron, T. Hastie, I. Johnstone and R. Tibshirani," Ann. Stat. 32(2), 469-475 (2004).