Image reconstruction from limited-view projections by convex nonquadratic spline regularization

Optical Engineering

Volumn 49, Issue 3, 2010, Pages

  Nguyen, Van Giang ^a   Lee, Soo Jin ^a  

^a PaiChai University   (South Korea)

Author keywords

Bayesian methods; Convex optimization; Image reconstruction; Limited angle tomography; Regularization; Spline energy

Indexed keywords

BAYESIAN METHODS; BLOCK SEQUENTIAL REGULARIZED EXPECTATION MAXIMIZATIONS; GEOMETRIC DISTORTION; GLOBALLY CONVERGENT; LIMITED-ANGLE TOMOGRAPHY; LINEAR COMBINATIONS; PENALTY FUNCTION; REGULARIZATION METHODS; SECOND ORDERS; SPATIAL DERIVATIVES; STREAK ARTIFACTS;

BAYESIAN NETWORKS; IMAGE RECONSTRUCTION; OPTIMIZATION; REPAIR; SPLINES; TOMOGRAPHY;

CONVEX OPTIMIZATION;

EID: 77949675466     PISSN: 00913286     EISSN: 15602303     Source Type: Journal    
DOI: 10.1117/1.3339871     Document Type: Article

References (21)

1. J. S. Karp, G. Muehllehner, D. A. Mankoff, C. E. Ordonez, J. M. Ollinger, M. E. Daube-Witherspoon, A. T. Haigh, and D. J. Beerbohm, "Continuous- slice PENN-PET: a positron tomograph with volume imaging capability, " J. Nucl. Med. 31(5) 617-627 (1990).
2. P. E. Kinahan, J. A. Fessler, and J. S. Karp, "Statistical image reconstruction methods in PET with compensation for missing data, " IEEE Trans. Nucl. Sci. 44(4) 1552-1557 (1997).
3. K. M. Hanson, "Bayesian and related methods in image reconstruction from incomplete data, " in Image Recovery: Theory and Application, H. Stark, Ed., pp. 79-127, Academic, New York (1987).
4. J. S. Jaffe, "Limited angle reconstruction using stabilized algorithms, " IEEE Trans. Med. Imaging 9(3) 338-344 (1990).
5. A. H. Delaney and Y. Bresler, "Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography, " IEEE Trans. Image Process. 7(2) 204-221 (1998).
6. S. Siltanen, V. Kolehmainen, S. Järvenpää, J. P. Kaipio, P. Koistinen, M. Lassas, J. Pirttilä, and E. Somersalo, "Statistical inversion for medical X-ray tomography with few radiographs: I. General theory, " Phys. Med. Biol. 48(10) 1437-1463 (2003).
7. M. Rantala, S. Vänskä, S. Järvenpää, M. Kalke, M. Lassas, J. Moberg, and S. Siltanen, "Wavelet-based reconstruction for limitedangle X-ray tomography, " IEEE Trans. Med. Imaging 25(2) 210-217 (2006).
8. M. Defrise, F. Noo, R. Clackdoyle, and H. Kudo, "Truncated Hilbert transform and image reconstruction from limited tomographic data, " Inverse Probl. 22, 1037-1053 (2006).
9. H. Y. Liao and G. Sapiro, "Sparse representations for limited data tomography, " in Proc. IEEE Int. Symp. Biomedical Imaging, pp. 1375-1378 (2008).
10. G. T. Herman and R. Davidi, "Image reconstruction from a small number of projections, " Inverse Probl. 24, 045011:1-17 (2008).
11. V. Kolehmainen, M. Lassas, and S. Siltanen, "Limited data X-ray tomography using nonlinear evolution equations, " SIAM J. Sci. Comput. 30(3) 1413-1429 (2008).
12. S.-J. Lee, "Simultaneous reconstruction and edge detection of tomographic images using accelerated deterministic annealing, " Opt. Eng. 46(5) 057006:1-10 (2007).
13. C. A. Bouman and K. Sauer, "A generalized Gaussian image model for edge-preserving MAP estimation, " IEEE Trans. Image Process. 2(3) 296-310 (1993).
14. S.-J. Lee, "Performance comparison of convex-nonquadratic priors for Bayesian tomographic reconstruction, " J. Electron. Imaging 9(3) 242-250 (2000).
15. P. J. Green, "Bayesian reconstruction from emission tomography data using a modified EM algorithm, " IEEE Trans. Med. Imaging 9(1) 84-93 (1990).
16. J. Browne and A. R. De Pierro, "A row-action alternative to the EM algorithm for maximizing likelihoods in emission tomography, " IEEE Trans. Med. Imaging 15(5) 687-699 (1996).
17. A. R. De Pierro and M. E. B. Yamagishi, "Fast EM-like methods for maximum 'a posteriori' estimates in emission tomography, " IEEE Trans. Med. Imaging 20(4) 280-288 (2001).
18. S. Ahn and J. A. Fessler, "Globally convergent image reconstruction for emission tomography using relaxed ordered subsets algorithms, " IEEE Trans. Med. Imaging 22(5) 613-626 (2003).
19. S.-J. Lee, G. R. Gindi, I. G. Zubal, and A. Rangarajan, "Using ground-truth data to design priors in Bayesian SPECT reconstruction, " in Information Processing in Medical Imaging, Y. Bizais, C. Barillot, and R. D. Paola, Eds., pp. 27-38, Kluwer, Norwell, MA (1995).
20. G. Chinn and S.-C. Huang, "Noise and resolution of Bayesian reconstruction for multiple image configurations, " IEEE Trans. Nucl. Sci. 40(6) 2059-2063 (1993).
21. S.-J. Lee, "Training set approach to smoothing parameter estimation for spline-regularized tomographic reconstruction, " Opt. Eng. 48(2) 027003 (2009).