Covariance-preconditioned iterative methods for nonnegatively constrained astronomical imaging

SIAM Journal on Matrix Analysis and Applications

Volumn 27, Issue 4, 2006, Pages 1184-1197

  Bardsley, Johnathan M ^a   Nagy, James G ^b  

^a UNIVERSITY OF MONTANA   (United States)

^b EMORY UNIVERSITY   (United States)

Author keywords

Image restoration; Linear models; Preconditioning; Statistical methods; Weighted least squares

Indexed keywords

ASTRONOMICAL IMAGING; LINEAR MODELS; WEIGHTED LEAST SQUARES;

ALGORITHMS; ASTRONOMY; CONSTRAINT THEORY; IMAGE RECONSTRUCTION; STATISTICAL METHODS; VECTOR QUANTIZATION;

ITERATIVE METHODS;

EID: 33750149637     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/040615043     Document Type: Conference Paper

References (19)

1. J. M. BARDSLEY AND C. R. VOGEL, A nonnegatively constrained convex programming method for image reconstruction, SIAM. J. Sci. Comput., 25, pp. 1326-1343.
2. M. BERTERO AND P. BOCCACCI, Introduction to Inverse Problems in Imaging, IOP Publishing Ltd., London, 1998.
3. D. CALVETTI, B. LEWIS, L. REICHEL, AND F. SGALLARI, Tikhonov regularization with nonnegativity constraint, Electron. Trans. Numer. Anal., 18 (2004), pp. 153-173.
4. R. H. CHAN AND M. K. No, Conjugate gradient methods for Toeplitx systems, SIAM Rev., 38 (1996), pp. 427-482.
5. H. W. ENGL, M. HANKE, AND A. NEUBAUER, Regularization of Inverse Problems, Kluwer Academic Publishers, Dordrecht, 2000.
6. W. FELLER, An Introduction to Probability Theory and Its Applications, Wiley, New York, 1971.
7. J. A. FESSLER, Penalized weighted least-squares image reconstruction for positron emission tomography, IEEE Trans. Med. Imag., 13 (1994), pp. 290-300.
8. G. H. GOLUB AND C. VAN LOAN, Matrix Computations, 3rd ed., Johns Hopkins Press, Baltimore, MD 1996.
9. M. HANKE AND J. G. NAGY, Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques, Inverse Problems, 12 (1996), pp. 157-173.
10. M. HANKE, J. G. NAGY, AND R. J. PLEMMONS, Preconditioned iterative regularization for illposed problems, in Numerical Linear Algebra, L. Reichel, A. Ruttan and R. S. Varga, eds., de Gruyter, Berlin, 1993, pp. 141-163.
11. P. C. HANSEN, Rank-Deficient and Discrete Ill-Posed Problems, SIAM, Philadelphia, 1997.
12. L. KAUFMAN, Maximum likelihood, least squares, and penalized least squares for PET, IEEE Trans. Med. Imag., 12 (1993), pp. 200-214.
13. J. G. NAGY, K. PALMER, AND L. PERRONE, Iterative methods for image restoration: A Matlab object oriented approach, Numer. Algorithms, 36 (2003), pp. 73-93.
14. J. NAGY AND Z. STRAKOŠ, Enforcing nonnegativity in image reconstruction algorithms, in Mathematical Modeling, Estimation, and Imaging, David C. Wilson et al., eds., SPIE, Bellingham, WA, 2000, pp. 182-190.
15. Y. SAAD, Iterative Methods for Sparse Linear Systems, PWS Publishing Company, Boston, 1996.
16. D. L. SNYDER, A. M. HAMMOUD, AND R. L. WHITE, Image recovery from data acquired with a charge-coupled-device camera, J. Opt. Soc. Amer. A, 10 (1993), pp. 1014-1023.
17. D. L. SNYDER, C. W. HELSTROM, A. D. LANTERMAN, M. FAISAL, AND R. L. WHITE, Compensation for readout noise in CCD images, J. Opt. Soc. Amer. A, 12 (1995), pp. 272-283.
18. R. Vio, J. BARDSLEY, AND W. WAMSTEKER, Least-squares methods with Poissonian noise: An analysis and a comparison with the Richardson-Lucy algorithm, Astronomy and Astrophysics, 437 (2005), pp. 741-755.
19. C. R. Vogel, Computational Methods for Inverse Problems, SIAM, Philadelphia, 2002.