Penalized maximum likelihood image restoration with positivity constraints: Multiplicative algorithms

Inverse Problems

Volumn 18, Issue 5, 2002, Pages 1397-1419

  Lantéri, Henri ^a   Roche, Muriel ^a   Aime, Claude ^a  

^a UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; GAUSSIAN NOISE (ELECTRONIC); MAXIMUM LIKELIHOOD ESTIMATION; PHOTODETECTORS; SPACE TELESCOPES;

MULTIPLICATIVE ALGORITHMS;

IMAGE RECONSTRUCTION;

EID: 0036796491     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/18/5/313     Document Type: Article

References (61)

1. Aime C. 2001 Teaching astronomical speckle techniques Eur. J. Phys. 22 169-84.
2. Avriel M. 1976 Non Linear Programming (Englewood Cliffs, NJ: Prentice-Hall).
3. Armijo L. 1966 Minimization of functions having continuous derivatives Pac. J. Math. 16 1-3.
4. Bertero M. and Boccacci P. 1998 Introduction to Inverse Problems in Imaging (Bristol: Institute of Physics Publishing).
5. Bertero M. 1989 Linear inverses and ill-posed problems Adv. Electron. Electron Phys. 75 1-121.
6. Bertero M., Boccacci P. and Maggio F. 1995 Regularization methods in image restoration: an application to HST images Int. J. Imaging Syst. Technol. 6 376-86.
7. Bertsekas D.P. 1995 Non-linear Programming (Belmont, MA: Athena Scientific).
8. Bouman C.A. and Saner K. 1996 A unified approach to statistical tomography using coordinate descent optimization IEEE Trans. Image Process. 5 480-92.
9. Butler C.S. and Miller M.I. 1993 Maximum a posteriori estimation for SPECT using regularization techniques on massively parallel computers IEEE Trans. Med. Imaging 12 84-9.
10. Byrne C.L. 1993 Iterative image reconstruction algorithms based on cross-entropy minimization IEEE Trans. Image Process. 2 96-103.
11. Combettes P.L. 1993 The foundations of set theoretic estimation Proc. IEEE 81 182-208.
12. Csiszár I. 1991 Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems Ann. Stat. 19 2032-66.
13. Daube-Witherspoon M.E. and Muehllehner G. 1986 An iterative image space reconstruction algorithm suitable for volume ECT IEEE Trans. Med. Imaging 5 61-6.
14. Demoment G. 1989 Image reconstruction and restoration: overview of common estimation structures and problems IEEE Trans. Acoust. Speech Signal Process. 37 2024-36.
15. Dempster A.D., Larid N.M. and Rubin D.B. 1977 Maximum likelihood from incomplete data via the EM algorithm J. R. Stat. Soc. B 39 1-37.
16. De Pierro A.R. 1987 On the convergence of the iterative image space reconstruction algorithm for volume ECT IEEE Trans. Med. Imaging 6 124-5.
17. De Pierro A.R. 1990 Nonlinear relaxation methods for solving symmetric linear complementarity problems J. Optim. Theory Appl. 64 87-99.
18. De Pierro A.R. 1993 On the relation between the ISRA and the EM algorithms for positron emission tomography IEEE Trans. Med. Imaging 12 328-33.
19. De Pierro A.R. 1995 A modified expectation maximization algorithm or penalized Likelihood estimation in emission tomography IEEE Trans. Med. Imaging 14 132-7.
20. De Pierro A.R. 1995 On the convergence of an EM type algorithm for penalized likelihood estimation in emission tomography IEEE Trans. Med. Imaging 14 762-5.
21. Eggermont P.P.B. 1990 Multiplicative iterative algorithms for convex programming Linear Algebr. Appl. 130 25-42.
22. Fessler J.A. and Hero A.O. 1994 Space alternating generalized expectation - maximization algorithm IEEE Trans. Acoust. Speech Signal Process. 42 2664-77.
23. Fessler J.A. and Hero A.O. 1995 Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithm IEEE Trans. Acoust. Speech Signal Process. 4 1417-29.
24. Goldstein A.A. 1967 Constructive Real Analysis (New York: Harper and Row).
25. Grenander U. 1981 Abstract Inference (New York: Wiley).
26. Hildebrand F.B. 1974 Introduction to Numerical Analysis (New York: McGraw-Hill).
27. Home K. 1985 Images of accretion discs-the eclipse mapping method Mon. Not. R. Astron. Soc. 213 129-41.
28. Katsaggelos A.K. and Lay K.T. 1991 Maximum likelihood identification and restoration of images using the expectation-maximization algorithm Digital Image Restoration (Springer Series in Information Sciences No 23) ed A.K. Katsaggelos (Heidelberg: Springer) ch 6.
29. Katsaggelos A.K. 1991 Introduction in Digital Image Restoration (Springer Series in Information Sciences No 23) ed A.K. Katsaggetos (Heidelberg: Springer) ch 1.
30. Lagendijk R.L. and Biemond J. 1991 Iterative Identification and Restoration of Images (London: Kluwer).
31. Lane R.G. 1996 Methods for maximum-likelihood deconvolution J. Opt. Soc. Am. A 13 1992-8.
32. Lantéri H., Soummer R. and Aime C. 1998 ISRA and RL algorithms used for deconvolution of AO and HST images ESO/OSA Topical Meeting on Astronomy with Adaptive Optics: Present Results and Future Programs (Sonthofen, Germany Sept. 1998) ed D. Bonaccini (Garching, Germany: ESO) pp 275-85.
33. Lantéri H., Soummer R. and Aime C. 1999 Comparison between ISRA and RLA. Use of a wiener filter based stopping criterion Astron. Astrophys. Suppl. Ser. 140 235-46.
34. Lantéri H., Roche M., Cuevas O. and Aime C. 1999 Maximum likelihood constrained regularized algorithms. An objective criterion for the determination of regularization parameters Eur. Symp. on Satellite and Remote Sensing (Florence Sept. 1999) vol 3866 (Bellingham, WA: SPIE Optical Engineering Press) pp 144-55.
35. Lantéri H., Roche M., Cuevas O. and Aime C. 2001 A general method to devise maximum-likelihood signal restoration multiplicative algorithms with non-negativity constraints Signal Process. 81 945-74.
36. Lantéri H., Roche M., Gancherel P. and Aime C. 2002 Ringing reduction in image restoration algorithms using a constraint on the inferior bound of the solution Signal Process. at press.
37. Llacer J. and Nuñez J. 1990 Iterative maximum-likelihood and Bayesian algorithms for image reconstruction in astronomy Restoration of Hubble Space Telescope Images ed R.L. White and R.J. Allen (Baltimore, MD: Space Telescope Science Institute) pp 62-9.
38. Lucy L.B. 1974 An iterative technique for the rectification of observed distributions Astron. J. 79 745-54.
39. Lucy L.B. 1994 Optimum strategy for inverse problems in statistical astronomy Astron. Astrophys. 289 983-94.
40. Luenberger D.G. 1973 Introduction to Linear and Nonlinear Programming (Reading, MA: Addison-Wesley).
41. Minoux M. 1983 Programmation Mathématique-Théorie et Algorithmes vol 1 (Paris: Dunod).
42. Nowak R.D. and Kolaczyk E.D. 2000 A statistical multiscale framework for Poisson inverse problem IEEE Trans. Inf Theory 46 1811-25.
43. Nuñez J. and Llacer J. 1993 A general Bayesian image reconstruction algorithm with entropy prior. Preliminary application to HST data Publ. Astron. Soc. Pac. 105 1192-208.
44. Richardson W.H. 1972 Bayesian based iterative method of image restoration J. Opt. Soc. Am. 62 55-9.
45. Roche M. 2001 Déconvolution d'images en astrophysique-méthodologie algorithmique Thèse de Doctorat Université de Nice, Sophia Antipolis.
46. Sekko E., Thomas G. and Boukrouche A. 1999 A deconvolution technique using optimal Wiener filtering and regularization Signal Process. 72 23-32.
47. Shepp L.A. and Vardi Y. 1982 Maximum likelihood reconstruction for emission tomography IEEE Trans. Med. Imaging 6 113-22.
48. Snyder D.L. and Miller M.I. 1985 The use of sieves to stabilize the images produced with the EM algorithm for emission tomography IEEE Trans. Nucl. Sci. 32 3864-72.
49. Snyder D.L., Miller M.I., Thomas L.J. and Politte D.G. 1987 Noise and edge artifacts in maximum-likelihood reconstruction for emission tomography IEEE Trans. Med. Imaging 6 226-38.
50. Snyder D.L. 1990 Modification of the Richardson-Lucy iteration for restoring Hubble space telescope imagery Restoration of Hubble Space Telescope Images ed R.L. White and R.J. Allen (Baltimore, MD: Space Telescope Science Institute) pp 56-61.
51. Snyder D.L., Schultz T.J. and O'Sullivan J.A. 1992 Deblurring subject to non-negativity constraints IEEE Trans. Signal Process. 40 1143-50.
52. Thomas G. 1983 A positive optimal deconvolution procedure IEEE Int. Conf. on Acoust. Speech and Signal Process, (Boston) pp 651-4.
53. Thomas G. and Prost R. 1991 Iterative constrained deconvolution Signal Process. 23 89-98.
54. Tikhonov A. and Arsenin V. 1976 Méthodes de Résolution des Problèmes Mal-Posés (Moscow: Mir).
55. Titterington D.M. 1985 General structure of regularization procedures in image reconstruction Astron. Astrophys. 144 381-7.
56. Tom V.T., Quartieri T.F., Hayes M.H. and McClellan J.H. 1981 Convergence of iterative non-expansive signal reconstruction algorithms IEEE Trans. Acoust. Speech Signal Process. 29 1052-8.
57. Traub J.F. 1964 Iterative Methods for the Solutions of Equations (Englewood Cliffs, NJ: Prentice-Hall).
58. Twomey S. 1977 Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (New York: Elsevier).
59. Vardi Y., Shepp L.A. and Kanfmann L. 1985 A statistical model for positron emission tomography J. Am. Stat. Assoc. 80 8-37.
60. Youla D.C. and Webb H. 1982 Image restoration by the method of convex projections: Part 1-Theory IEEE Trans. Med. Imaging 1 81-94.
61. Zacchéo T.S. and Gonsalves R.A. 1996 Iterative maximum-likelihood estimators for positively constrained objects J. Opt. Soc. Am. A 13 236-42.