A Theoretical study of the contrast recovery and variance of MAP reconstructions from PET data

IEEE Transactions on Medical Imaging

Volumn 18, Issue 4, 1999, Pages 293-305

  Qi, Jinyi ^a,b   Leahy, Richard M ^a,b  

^a IEEE   (United States)

^b UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

Hyperparameter estimation; Image resolution; Map estimation; Variance analysis

Indexed keywords

ANALYSIS OF VARIANCE; ANIMAL; ARTICLE; COMPUTER ASSISTED EMISSION TOMOGRAPHY; NORMAL DISTRIBUTION; THEORETICAL MODEL;

ANALYSIS OF VARIANCE; ANIMALS; MODELS, THEORETICAL; NORMAL DISTRIBUTION; TOMOGRAPHY, EMISSION-COMPUTED;

APPROXIMATION THEORY; IMAGE ANALYSIS; IMAGE RECONSTRUCTION; MATHEMATICAL MODELS; MAXIMUM PRINCIPLE; OPTICAL RESOLVING POWER; POSITRON EMISSION TOMOGRAPHY;

CONTRAST RECOVERY COEFFICIENT (CRC); MAXIMUM A POSTERIORI (MAP) PRINCIPLES;

MEDICAL IMAGING;

EID: 0032589150     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/42.768839     Document Type: Article

References (37)

1. R. Huesman, "A new fast algorithm for the evaluation of regions of interest and statistical uncertainty in computed tomography," Phys. Med. Biol., vol. 29, pp. 543-552, 1984.
2. H. H. Barrett, D. W. Wilson, and B. M. W. Tsui, "Noise properties of the EM algorithm: I. Theory," Phys. Med. Biol., vol. 39, pp. 833-846, 1994.
3. L. Shepp and Y. Vardi, "Maximum likelihood reconstruction for emission tomography," IEEE Trans. Med. Imag., vol. 1, pp. 113-122, Oct. 1982.
4. D. W. Wilson, B. M. W. Tsui, and H. H. Barrett, "Noise properties of the EM algorithm: II. Monte Carlo simulations," Phys. Med. Biol., vol. 39, pp. 847-872, 1994.
5. W. Wang and G. Gindi, "Noise analysis of MAP-EM algorithms for emission tomography," Phys. Med. Biol., vol. 42, pp. 2215-2232, 1997.
6. K. Lange, M. Bahn, and R. Little, "A theoretical study of some maximum likelihood algorithms for emission and transmission tomography," IEEE Trans. Med. Imag., vol. 6, pp. 106-114, June 1987.
7. P. Green, "Bayesian reconstructions from emission tomography data using a modified EM algorithm," IEEE Trans. Med. Imag., vol. 9, pp. 84-93, Mar. 1990.
8. H. M. Hudson and R. S. Larkin, "Accelerated image reconstruction using ordered subsets of projection data," IEEE Trans. Med. Imag., vol. 13, pp. 601-609, 1994.
9. J. Fessier, "Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): Applications to tomography," IEEE Trans. Image Processing, vol. 5, pp. 493-506, Mar. 1996.
10. J. A. Fessier and W. L. Rogers, "Spatial resolution properties of penalized-likelihood image reconstruction: Spatial-invariant tomographs," IEEE Trans. Image Processing, vol. 9, no. 5, pp. 1346-1358, Sept. 1996.
11. J. A. Fessier, "Approximate variance images for penalized-likelihood image reconstruction," in Proc. IEEE Nuclear Science Symp. Medical Imaging Conf., Albuquerque, NM, 1997.
12. E. Mumcuoglu, R. Leahy, S. Cherry, and Z. Zhou, "Fast gradient-based methods for Bayesian reconstruction of transmission and emission PET images," IEEE Trans. Med. Imag., vol. 13, pp. 687-701, Dec. 1994.
13. C. Bouman and K. Sauer, "A unified approach to statistical tomography using coordinate descent optimization," IEEE Trans. Image Processing, vol. 5, pp. 480-492, Mar. 1996.
14. J. A. Fessier and A. O. Hero, "Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms," IEEE Trans. Image Processing, vol. 4, pp. 1417-1429, 1995.
15. K. Sauer and C. Bouman, "A local update strategy for iterative reconstruction from projections," IEEE Trans. Signal Processing, vol. 41, pp. 534-548, Feb. 1993.
16. J. A. Fessier, "Penalized weighted least squares image reconstruction for PET," IEEE Trans. Med. Imag., vol. 13, pp. 290-300, June 1994.
17. J. A. Fessier and S. D. Booth, "Conjugate-gradient preconditioning methods for shift-variant image reconstruction," IEEE Trans. Image Processing, to be published.
18. S. Geman and D. McClure, "Statistical methods for tomographic image reconstruction," in P roc. 46th Session ISI, vol. 52, 1987.
19. 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. Imag., vol. 16, pp. 516-526, 1997.
20. Z. Zhou, R. Leahy, and J. Qi, "Approximate maximum-likelihood hyperparameter estimation for Gibbs-priors," IEEE Trans. Image Processing, vol. 6, pp. 844-861, 1997.
21. P. Craven and G. Wahba, "Smoothing noisy data with spline function," Numerische Mathematik, vol. 31, pp. 377-403, 1979.
22. V. Johnson, "A model for segmentation and analysis of noisy images," Institute Stat. Decision Sci., Duke Univ., Discussion Paper 91-A151991.
23. M. Yavuz and J. A. Fessier, "Objective functions for tomographic reconstruction from randoms-precorrected PET scans," in Proc. IEEE Nuclear Science Symp. and Medical Imaging Conf., Anaheim, CA, 1996, vol. 2, pp. 1067-1071.
24. E. Mumcuoglu, R. Leahy, S. Cherry, and E. Huffman, "Accurate geometric and physical response modeling for statistical image reconstruction in high resolution PET," in Proc. IEEE Nuclear Science Symp. and Medical Imaging Conf., Anaheim, CA, 1996, pp. 1569-1573.
25. J. Qi, R. M. Leahy, S. R. Cherry, A. Chatziioannou, and T. H. Farquhar, "High resolution 3D Bayesian image reconstruction using the microPET small animal scanner," Phys. Med. Biol., vol. 43, no. 4, pp. 1001-1013, 1998.
26. J. Qi and R. M. Leahy, "Resolution and noise properties of map reconstruction for fully 3-D pet," in Proc. Int. Meeting Fully 3D Image Reconstruction Radiology Nuclear Medicine, 1999, to be published.
27. S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images," IEEE Trans. Pattern Anal. Machine Intell, vol. PAMI-6, pp. 721-741, Nov. 1984.
28. R. M. Kessler, J. R. Ellis Jr., and M. Eden, "Analysis of emission tomographic scan data: Limitations imposed by resolution and background," J. Comput. Assist. Tomogr., vol. 8, pp. 514-522, 1984.
29. L.-N. D. Loo, K. Doi, and C. E. Metz, "A comparison of physical image comparison indices and observer performance in the radiographie detection of nylon beads," Phys. Med. Biol., vol. 29, no. 7, pp. 837-857, 1984.
30. A. Rosenfeld and A. Kak, Digital Picture Processing, 2nd ed. New York: Academic, 1982, vol. 1.
31. A. O. Hero, J. A. Fessier, and M. Usman, "Exploring estimator biasvariance tradeoffs using the uniform CR bound," IEEE Trans. Signal Processing, vol. 44, pp. 2026-2041, Aug. 1996.
32. A. Blake and A. Zisserman, Visual Reconstruction. Cambridge, MA: MIT, 1987.
33. S.-J. Lee, A. Rangarajan, and G. Gindi, "Bayesian image reconstruction in SPECT using higher order mechanical models as priors," IEEE Trans. Med. Mag., vol. 14, pp. 669-680, Dec. 1995.
34. K. J. Myers, H. H. Barre, v M. C. Borgstrom, D. D. Patton, and G. W. Seeley, "Effect of noise correlation on detectability of disk signals in Med. Imag.," J. Opt. Soc. Amer. A, vol. 2, pp. 1752-1759, 1985.
35. J.-S. Liow and S. C. Strother, "Practical tradeoffs between noise, quantitation, and number of iterations for maximum likelihood-based reconstructions," IEEE Trans. Med. Imag., vol. 10, pp. 563-571, Dec. 1991.
36. E. Huffman, P. Cutler, W. Digby, and J. Mazziotta, "3D phantom to simulate cerebral blood flow and metabolic images for PET," IEEE Trans. Nucl. Sci., vol. 37, pp. 616-620, Apr. 1990.
37. R. Carson, Y. Yan, B. Chodkowski, T. Yap, and M. Daube-Witherspoon, "Precision and accuracy of regional radioactivity quantitation using the maximum likelihood EM reconstruction algorithm," IEEE Trans. Med. Imag., vol. 13, pp. 526-537, Sept. 1994.