Training set approach to smoothing parameter estimation for spline-regularized tomographic reconstruction

Optical Engineering

Volumn 48, Issue 2, 2009, Pages

  Lee, Soo Jin ^a  

^a PaiChai University   (South Korea)

Author keywords

Bayesian methods; emission computed tomography; Gibbs priors; image reconstruction; smoothing parameter; spline energy

Indexed keywords

BAYESIAN APPROACHES; BAYESIAN METHODS; CLOSED-LOOP; EMISSION COMPUTED TOMOGRAPHY; GIBBS PRIORS; GIBBS SAMPLING; IMAGING APPLICATIONS; MATHEMATICAL PHANTOMS; NUMERICAL EXPERIMENTS; PERCENTAGE ERROR; PERFORMANCE OF ALGORITHM; PRIOR PROBABILITY; PROJECTION DATA; SMOOTHING PARAMETER; SMOOTHING PARAMETER ESTIMATION; TOMOGRAPHIC RECONSTRUCTION; TRAINING DATA; TRAINING SETS;

ALGORITHMS; BAYESIAN NETWORKS; COMPUTERIZED TOMOGRAPHY; ESTIMATION; IMAGE RECONSTRUCTION; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; MEDICAL IMAGING; OPTIMIZATION; TOMOGRAPHY;

PARAMETER ESTIMATION;

EID: 77949749285     PISSN: 00913286     EISSN: 15602303     Source Type: Journal    
DOI: 10.1117/1.3080742     Document Type: Article

References (27)

1. J., Qi and R., Leahy, " Iterative reconstruction techniques in emission computed tomography, ", Phys. Med. Biol., 51, 541-577 (2006). pme PHMBA7 0031-9155
2. R. M., Lewitt and S., Matej, " Overview of methods for image reconstruction from projections in emission computed tomography, ", Proc. IEEE, 91 (10), 1588-1611 (2003). iee IEEPAD 0018-9219 10.1109/JPROC.2003.817882 (Pubitemid 40890806)
3. S., Geman and D., Geman, " Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, ", IEEE Trans. Pattern Anal. Mach. Intell., 6 (6), 721-741 (1984). ipa ITPIDJ 0162-8828 (Pubitemid 15453722)
4. S. J., Lee, A., Rangarajan, and G., Gindi, " Bayesian image reconstruction in SPECT using higher order mechanical models as priors, ", IEEE Trans. Med. Imaging, 14 (4), 669-680 (1995). itm ITMID4 0278-0062 10.1109/42.476108
5. S. J., Lee, I. T., Hsiao, and G. R., Gindi, " The thin plate as a regularizer in Bayesian SPECT reconstruction, ", IEEE Trans. Nucl. Sci., NS-44 (3), 1381-1387 (1997). ien IETNAE 0018-9499 10.1109/23.597017 (Pubitemid 127827103)
6. S. J., Lee, " Spline-regularized ordered subsets expectation maximization algorithms for emission computed tomography, ", J. Electron. Imaging, 12 (1), 17-24 (2003). jei JEIME5 1017-9909 10.1117/1.1525791
7. S., Geman and D. E., McClure, " Statistical methods for tomographic image reconstruction, ", Bull. Internat. Statist. Inst., LII-4, 5-21 (1987). c3k BIISAR 0074-8609
8. N. P., Galatsanos and A. K., Katsaggelos, " Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation, ", IEEE Trans. Image Process., 1 (3), 322-336 (1992). iei IIPRE4 1057-7149 10.1109/83.148606
9. P. C., Hansen, " Analysis of discrete ill-posed problems by means of the L-curve, ", SIAM Rev., 34 (4), 561-580 (1992). sir SIREAD 0036-1445 10.1137/1034115
10. Z., Zhou, R. M., Leahy, and E. U., Mumcuoglu, " Maximum likelihood hyperparameter estimation for Gibbs priors with applications to PET, " in, Information Processing in Medical Imaging, Y., Bizais, C., Barillot, and, R. D., Paola, Eds., pp. 39-51, Kluwer, Norwell, MA (1995).
11. 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).
12. J. A., Fessler and W. L., Rogers, " Spatial resolution properties of penalized-likelihood image reconstruction: spatial-invariant tomographs, ", IEEE Trans. Med. Imaging, 9 (10), 1346-1358 (1996). itm ITMID4 0278-0062 (Pubitemid 126782391)
13. D. M., Higdon, J. E., Bowsher, V. E., Johnson, T. G., Turkington, D. R., Gilland, and R. J., Jaszczak, " Fully Bayesian estimation of Gibbs hyperparameters for emission computed tomography data, ", IEEE Trans. Med. Imaging, 16 (5), 516-526 (1997). itm ITMID4 0278-0062 10.1109/42.640741 (Pubitemid 127767630)
14. Z., Zhou, R. M., Leahy, and J., Qi, " Approximate maximum likelihood hyperparameter estimation for Gibbs priors, ", IEEE Trans. Image Process., 6 (6), 844-861 (1997). iei IIPRE4 1057-7149 10.1109/83.585235 (Pubitemid 127768398)
15. J., Qi and R. M., Leahy, " A theoretical study of the contrast recovery and variance of MAP reconstructions from PET data, ", IEEE Trans. Med. Imaging, 18 (4), 293-305 (1999). itm ITMID4 0278-0062
16. N. P., Galatsanos, V. Z., Mesarovic, R., Molina, A. K., Katsaggelos, and J., Mateos, " Hyperparameter estimation in image restoration problems with partially known blurs, ", Opt. Eng., 41 (8), 1845-1854 (2002). gar OPEGAR 0091-3286 10.1117/1.1487850 (Pubitemid 35019748)
17. B. M., Graham and A., Adler, " Objective selection of hyperparameter for EIT, ", Physiol. Meas, 27, S65-S79 (2006). 3nk ZZZZZZ 0967-3334
18. S., Geman and C., Graffigne, " Markov random fields image models and their application to computer vision, " in, Proc. Intl. Congress of Mathematicians 1986, A. M., Gleason, Ed., pp. 1496-1517, American Mathematical Society, Providence, (1987).
19. J., Besag, " On the statistical analysis of dirty pictures, ", J. R. Stat. Soc. Ser. B (Methodol.), 48 (3), 259-302 (1986). 9gx JSTBAJ 0035-9246
20. D., Dougherty, I. T., Hsiao, and G. R., Gindi, " Computerized biological brain phantom for evaluation of PET and SPECT reconstruction, ", IEEE Trans. Nucl. Sci., 45 (3), 1238-1243 (1998). ien IETNAE 0018-9499 (Pubitemid 128739189)
21. J., Besag, " Spatial interaction and the statistical analysis of lattice systems, ", J. R. Stat. Soc. Ser. B (Methodol.), 36, 192-236 (1974). 9gx JSTBAJ 0035-9246
22. W. E. L., Grimson, From Surfaces to Images, The MIT Press, Cambridge, MA, (1981).
23. D., Terzopoulos, " Multilevel computational processes for visual surface reconstruction, ", Comput. Vis. Graph. Image Process., 24, 52-96 (1983). cvg CVGPDB 0734-189X 10.1016/0734-189X(83)90020-8 (Pubitemid 14466542)
24. D., Terzopoulos, " Regularization of inverse visual problems involving discontinuities, ", IEEE Trans. Pattern Anal. Mach. Intell., 8, 413-424 (1986). ipa ITPIDJ 0162-8828 (Pubitemid 16614037)
25. M., Gokmen and A. K., Jain, " λτ -space representation of images and generalized edge detector, ", IEEE Trans. Pattern Anal. Mach. Intell., 19 (6), 545-563 (1997). ipa ITPIDJ 0162-8828 10.1109/34.601227 (Pubitemid 127762250)
26. G., Chinn and S. C., Huang, " Noise and resolution of Bayesian reconstruction for multiple image configurations, ", IEEE Trans. Nucl. Sci., 40, 2059-2063 (1993). ien IETNAE 0018-9499 10.1109/23.273561
27. J. L., Lear, " Principles of single and multiple radionuclide autoradiography, " in, Positron Emission Tomography and Autoradiography, Chap. 5, M. E., Phelps, J. C., Mazziotta, and, H. R., Schelbert, Eds., Raven Press, New York (1986).