PET Regularization by envelope guided conjugate gradients

IEEE Transactions on Medical Imaging

Volumn 15, Issue 3, 1996, Pages 385-389

  Kaufman, Linda ^a   Neumaier, Arnold ^b  

^a LUCENT TECHNOLOGIES   (United States)

^b UNIVERSITY OF VIENNA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

IMAGE RECONSTRUCTION; ITERATIVE METHODS; OPTIMIZATION; PROBLEM SOLVING;

ENVELOPE GUIDED CONJUGATE GRADIENTS; MULTIOBJECTIVE OPTIMIZATION; PRECONDITIONED CONJUGATE GRADIENT ITERATION; TIKHONOV REGULARIZATION;

POSITRON EMISSION TOMOGRAPHY;

EID: 0030171318     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/42.500147     Document Type: Article

References (16)

1. S. Gcman and D. McClure, "Bayesian image analysis: An application te single photon emission tomography," in froc. Stat.. Comput. Sect., Amer. Stal.. Assoc.. Washington, DC, 1985. pp. 12-18.
2. P. Green, "Bayesian reconstructions from emission tomography using a modified EM algorithm," IEEE Trans. Med. Imag., vol. 9, pp. 84-93, 1990.
3. M. Hanke and P. C. Hansen, "Regularization methods for large-scale problems," Sun. Math. Ind., vol. 3, pp. 253-315, 1993.
4. P. C. Hansen, "Analysis of discrete ill-posed problems by means of the L-curve," SI AM Rev., vol. 34, pp. 561-580, 1992.
5. P. C. Hansen and D. P. O'Leary, "The use of the L curve in the regularization of discrete ill-posed problems,'' SIAM J. Sei. Comput., vol. 14, pp. 1487-1506, 1993.
6. T. Hebert and R. Leahy, "A generalized F.M algorithm for the 3-D Bayesian reconstruction from Poisson data using Gibbs priors,'' IEEE Trans. Med. Imag.. vol. 8, pp. 194-202, 1990.
7. P. J. Huber, Robust Statistics. New York: Wiley, 1981.
8. L. Kaufman, "Maximum likelihood, least squares, and penali/ed least squares for PET," IEEE Trans. Med. Imag., vol. 12, pp. 200-214, 1993.
9. L. Kaufman and A. Neumaier, "Image reconstruction through regularization by envelope guided conjugate gradients," AT&T Bell Laboratories, Murray Hill, NJ, Tech. Rep. CS94/4-14.1994. (available through the WWW, http://netlib.att.com/netlib/att/cs/doc/94/4-14.ps, 2MB)
10. D. S. Lalush and B. M. W. Tsui, "Simulation evaluation of Gibbs prior distributions for use in maximum a posteriori SPECT reconstructions," IEEE Trans. Med. Imag., vol. 11, pp. 267-275, 1992.
11. K. Lange and J. Fessier, "Globally convergent algorithms for maximum a posteriori transmission tomography," IEEE Trans. Image. Processing, vol. 4, 1995.
12. C. L. Lawson and R. J. Hanson, Solving Least Squares Problems. Englcwood Cliffs, NJ: Prentice-Hal], 1974
13. L. Shepp and Y. Vardi, "Maximum likelihood reconstruction in positron emission tomography," I EKE Trans. Med. Imag., vol. MI-1, pp. 113-122, 1982.
14. M. Symonds, Y.-S. Han, P. Santago, and W. Snyder, "Reconstruction of positron emission tomography images by using maximum a posteriori and mean field annealing techniques," in P rue. SPIE: Physics of Med. Imag., 19, vol. 2613, pp. 212-222.
15. C. R. Vogel and VI. E. Oman, "Iterative methods for total variation denoising," SIAM J. Sei. Comput, vol. 17, pp. 227-238, 1996.
16. G. Wahba, "Practical approximate solutions to linear operator equations when the data are noisy," SIAM J. Numer. Anal, vol. 14, pp. 651-657, 1977.