Image reconstruction exploiting object sparsity in boundary-enhanced X-ray phase-contrast tomography

Optics Express

Volumn 18, Issue 10, 2010, Pages 10404-10422

  Sidky, Emil Y ^a   Anastasio, Mark A ^b   Pan, Xiaochuan ^a  

^a UNIVERSITY OF CHICAGO   (United States)

^b Illinois Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DATA FLOW ANALYSIS; IMAGE RECONSTRUCTION; LIGHT REFRACTION; REFRACTIVE INDEX; REFRACTOMETERS; REPAIR; TOMOGRAPHY;

DATA CONSISTENCY; ITERATIVE ALGORITHM; PROJECTION DATA; RECONSTRUCTION ALGORITHMS; REFRACTIVE-INDEX DISTRIBUTION; X-RAY PHASE-CONTRAST TOMOGRAPHY;

ALGORITHMS;

ALGORITHM; ARTICLE; COMPUTER ASSISTED DIAGNOSIS; METHODOLOGY; REFRACTOMETRY; TOMOGRAPHY; X RAY DIFFRACTION;

ALGORITHMS; IMAGE INTERPRETATION, COMPUTER-ASSISTED; REFRACTOMETRY; TOMOGRAPHY; X-RAY DIFFRACTION;

EID: 77952706506     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.18.010404     Document Type: Article

References (40)

1. A. Barty, K. Nugent, A. Roberts, and D. Paganin, "Quantitative phase tomography," Opt. Commun. 175(4), 329-336 (2000).
2. T. Weitkamp, C. Rau, A. Snigirev, B. Brenner, T. Gunzler, M. Kuhlmann, and C. Schroer, "In-line phase contrast in synchrotron-radiation microradiography and tomography," in Developments in X-ray Tomography III, Proceedings of the SPIE, vol. 4503, pp. 92-102 (2002).
3. P. Cloetens, R. Barrett, J.-P. Guigay, and M. Schlenker, "Phase objects in synchrotron radiation hard x-ray imaging," J. Phys. D: Appl. Phys. 29, 133-146 (1996).
4. A. V. Bronnikov, "Theory of quantitative phase-contrast computed tomography," J. Opt. Soc. Am. A 19(3), 472-480 (2002).
5. T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterest, and S. W. Wilkins, "Phase-and-amplitude computer tomography," Appl. Phys. Lett. 89, 034,102 (2006).
6. M. A. Anastasio, D. Shi, Y. Huang, and G. Gbur, "Image Reconstruction in Spherical Wave Intensity Diffraction Tomography," J. Opt. Soc. Am. A 22, 2651-2661 (2005).
7. P. Cloetens, M. Pateyron-Salome, J. Y. Buffiere, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, "Observation of microstructure and damage in materials by phase sensitive radiography and tomography," J. Appl. Phys. 81, 5878-5886 (1997).
8. P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, "In-line holography and phase-contrast microtomography with high energy x-rays," Phys. Med. Biol. 44(3), 741-749 (1999).
9. E. F. Donnelly, R. R. Price, K. G. Lewis, and D. R. Pickens, "Polychromatic phase-contrast computed tomography," Med. Phys. 34(8), 3165-3168 (2007).
10. G. R. Myers, D. M. Paganin, T. Gureyev, and S. C. Mayo, "Phase-contrast tomography of single-material objects from few projections," Opt. Express 16, 908-919 (2008).
11. G. R. Myers, T. E. Gureyev, D. M. Paganin, and S. C. Mayo, "The binary dissector: phase contrast tomography of two- and three-material objects from few projections," Opt. Express 16, 10736-10749 (2008).
12. M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, "Analytic image reconstruction in local phase-contrast tomography," Phys. Med. Biol. 49, 121-144 (2004).
13. D. Shi, M. Anastasio, and X. Pan, "Reconstruction of refractive index discontinuities from truncated phase-contrast tomography projections," Appl. Phys. Lett. 86, 034102 (2005).
14. Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, "A high-throughput x-ray microtomography system at the Advanced Photon Source," Rev. Sci. Instrum. 72, 2062-2068 (2001).
15. E. Candes, J. Romberg, and T. Tao, "Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory 52, 3526-3530 (2006).
16. A. Pogany, D. Gao, and S. W. Wilkins, "Contrast and resolution in imaging with a microfocus x-ray source," Rev. Sci. Instrum. 68, 2774-2782 (1997).
17. T. E. Gureyev and S. W. Wilkins, "On x-ray phase imaging with a point source," J. Opt. Soc. Am. A 15(3), 579-585 (1998).
18. F. Natterer, The Mathematics of Computerized Tomography (Wiley, New York, 1986).
19. M. Liebling, T. Blu, and M. Unser, "Fresnelets: New Multiresolution Wavelet Bases for Digital Holography," IEEE Trans. Image Process. 12(1), 29-43 (2003).
20. H. Barrett and K. Myers, Foundations of Image Science (Wiley Series in Pure and Applied Optics, 2004).
21. A. Kak and M. Slaney, Principles of Computerized Tomographic. Imaging (IEEE Press, 1988).
22. J. Tropp, "Just relax: Convex programming methods for identifying sparse signals," IEEE Trans. Info. Theory 51, 1030-1051 (2006).
23. E. Y. Sidky, R. Chartrand, and X. Pan, "Image reconstruction from few views by non-convex optimization," IEEE Nuc. Sci. Conf. Rec. 5, 3526-3530 (2007).
24. R. Baraniuk, "Compressive Sensing," IEEE Sig. Process. Mag. 24, 118-121 (2007).
25. M. A. Figueiredo, R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE J. Sel. Top. Sig. Process. 1, 586-598 (2007).
26. M. Li, H. Yang, and H. Kudo, "An accurate iterative reconstruction algorithm for sparse objects: Application to 3D blood vessel reconstruction from a limited number of projections," Phys. Med. Biol. 47, 2599-2609 (2002).
27. S. Chen, D. Donoho, and M. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput. 20, 33-61 (1998).
28. F. Santosa and W. Symes, "Linear inversion of band-limited reflection, histograms," SIAM. J. Sci. Stat. Comput. 7, 1307-1330 (1986).
29. W. Souidene, A. Aissa-El-Bey, K. Abed-Meraim, and A. Beghdadi, "Blind Image Separation using Sparse Representation," in ICIP 2007. IEEE International Conference on Image Processing, vol. 3, pp. III -125-III -128 (2007).
30. E. Y. Sidky, C.-M. Kao, and X. Pan, "Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT," J. X-ray Sci. Tech. 14, 119-139 (2006).
31. E. Y. Sidky and X. C. Pan, "Image reconstruction, in circular cone-beam computed tomography by constrained, total-variation minimization," Phys. Med. Biol. 53, 4777-4807 (2008).
32. G.-H. Chen, J. Tang, and S. Leng, "Prior image constrained compressed sensing (PICCS): A method to accurately reconstruct dynamic CT images from highly undersampled projection data sets," Med. Phys. 35(2), 660-663 (2008).
33. R. Chartrand, "Exact reconstruction of sparse signals via nonconvex minimization," IEEE Sig. Process. Lett. 14, 707-710 (2007).
34. T. Blumensath and M. Davies, "Iterative hard thresholding for compressed sensing," Applied and Computational Harmonic Analysis 27, 265-274 (2009).
35. E. J. Candès and M. B. Wakin, "An Introduction To Compressive Sampling," IEEE Sig. Proc. Mag. 25, 21-30 (2008).
36. R. Garg and K. Khandekar, "Gradient Descent with Sparsification: An iterative algorithm for sparse recovery with restricted isometry property," Proceedings of the 26th Annual International Conference on Machine Learning 382, 337-344 (2009).
37. C. Hamaker and D. C. Solmon, "Angles between, null spaces of x-rays," J. Math. An. App. 62, 1-23 (1978).
38. G. T. Herman and L. B. Meyer, "Algebraic reconstruction techniques can be made computationally efficient," IEEE Trans. Med. Imag. 12, 600-609 (1993).
39. H. Q. 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. 39, 2005-2022 (1994).
40. X. Pan, E. Y. Sidky, and M. Vannier, "Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?" Inv. Prob. 25, 123009 (2009).