Iterative Methods for Image Deblurring

Proceedings of the IEEE

Volumn 78, Issue 5, 1990, Pages 856-883

  Biemond, Jan ^a   Lagendijk, Reginald L ^a   Mersereau, Russell M ^b  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES--ITERATIVE METHODS; PHOTOGRAPHIC REPRODUCTION; SIGNAL FILTERING AND PREDICTION;

CONVOLUTION INTEGRAL; IMAGE DEBLURRING; INVERSE FILTERS; PHOTOGRAPHIC IMAGES; WIENER FILTERS;

IMAGE PROCESSING;

EID: 0025430595     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/5.53403     Document Type: Article

References (99)

1. R. W. Schafer, R. M. Mersereau, and M. A. Richards, “Constrained iterative signal restoration algorithms,” Proc. IEEE, vol. 69, pp. 432–450, Apr. 1981.
2. J. L. C.Sanz and T. S. Huang, “Unified Hubert space approach to iterative least-squares linear signal restoration,” J. Opt. Soc. Amer., vol. 73, pp. 1455–1465, Nov. 1983.
3. Y. Ichioka and N. Nakajima, “Iterative image restoration considering visibility,” J. Opt. Soc. Amer., vol. 71, pp. 983–988, Aug. 1981.
4. H. J. Trussell, “Convergence criteria for iterative restoration methods,” IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-31, pp. 129–136, Feb. 1983.
5. H. J. Trussell and M. R. Civanlar, “The feasible solution in signal restoration,” IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-32, pp. 201–212, Apr. 1984.
6. D. C. Youla and H. Webb, “Image restoration by the method of convex projections: Part 1–Theory,” IEEE Trans. Med. Imaging, vol. MM, pp. 81–94, Oct. 1982.
7. M. I. Sezan and H. Stark, “Image restoration by the method of convex projections: Part 2—Applications and numerical results,” IEEE Trans. Med. Imaging, vol. MM, pp. 95–101, Oct. 1982.
8. V. T. Tom, T. F. Quatieri, M. H. Hayes, and J. H. McClellan, “Convergence of iterative non-expansive signal restoration algorithms,” IEEE Trans. Acoust., Speech, Signal Process., vol. ASSP-29, pp. 1052–1058, Oct. 1981.
9. A. K. Katsaggelos, J. Biemond, R. M. Mersereau, and R. W. Schafer, “An iterative method for restoring noisy blurred images,” Circ. Syst. Signal Proc., vol. 3, pp. 139–160, 1984.
10. S. Kawata and Y. Ichioka, “Iterative image restoration for linearly degraded images, I. Basis & II. Reblurring procedure,” J. Opt. Soc. Am., vol. 70, pp. 762-772, July 1980.
11. A. K. Katsaggelos, Constrained Iterative Restoration Algorithms, Ph.D. Thesis, Georgia Institute of Technology, 1985.
12. A. Levi and H. Stark, “Image restoration by the method of generalized projections with applications to restoration from magnitude,” J. Opt. Soc. Am., vol. 74, pp. 932–943, Sept. 1984.
13. M. I. Sezan,A. M.Tekalp,and C.T.Chen, “Regularizedsignal restoration using the theory of convex projections,” Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, pp. 1565– 1568, 1987.
14. R. L. Lagendijk, J. Biemond, and D. E. Boekee, “Regularized iterative image restoration with ringing reduction,” IEEE Trans. Acoustics, Speech, Signal Processing, vol. ASSP-36, pp. 1874–1888, Dec. 1988.
15. A. K. Katsaggelos, J. Biemond, R. M. Mersereau, and R. W. Schafer, “Nonstationary iterative image restoration,” Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, 1985, pp. 696–699.
16. Y. Ichioka, Y. Takabo, K. Matsuoka, and T. Suzuki, “Iterative image restoration by a method of steepest descent,”J. Optics (Paris), vol. 12, pp. 35–41, 1981.
17. C. Ross, “Iterative methods in information processing for object restoration,” OpticaActa, vol. 29, no. 11, pp. 1523–1542, 1982.
18. A. K. Katsaggelos and R. W. Schafer, “Iterative deconvolution using different distorted versions of an unknown signal,” Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, 1983, pp. 659–662.
19. A. K. Katsaggelos, “A general formulation of adaptive iterative image restoration algorithms,” Proc. Princeton Conf. on Info. Sciences and Systems, 1986, pp. 42–46.
20. J. Maeda and K. Murata, “Restoration of band-limited images by an iterative regularized pseudoinverse method,” J. Opt. Soc. Amer. A, vol. 1, pp. 28–34, Jan. 1984.
21. R. J. Mammone and R. J. Rothacker, “General iterative method of restoring linearly degraded images,” J. Opt. Soc. Amer. A, vol. 4, no. 1, pp. 208–215, Jan. 1987.
22. H. C. Andrews and B. R. Hunt, Digital Image Restoration. Englewood Cliffs, NJ: Prentice-Hall, 1977.
23. J. Biemond, “Stochastic linear image restoration,” in Advances in Computer Vision and Image Processing, T. S. Huang, Ed. London: JAI Press Inc., ch. 5, vol. II, pp. 502–528, 1986.
24. J. W. Woods and V. K. Ingle, “Kalman filtering in two dimensions—Further results,” IEEE Trans. Acoustics, Speech, Signal Processing, vol. ASSP-29, pp. 188–197, Apr. 1981.
25. B. R. Hunt,“Theapplicationof constrained least-squares estimation to image restoration by digital computer,” IEEE Trans. Computers, vol. C-22, pp. 805–812, Sept. 1973.
26. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems. New York: Wiley, 1977.
27. K.Miller, “Least squares methods for ill-posed problems with a prescribed bound,” SIAM J. Math. Anal., vol. 1, pp. 52–74, Feb. 1970.
28. W. K. Pratt, “Vector space formulation of two-dimensional signal processing operations,” Computer Graphics and Image Processing, vol. 4, pp. 1–24, 1975.
29. A. K. Jain, “Advances in mathematical models for image processing,” Proc. IEEE, vol. 69, pp. 502–528, May 1981.
30. M. P. Ekstrom and J. W. Woods, “Two-dimensional spectral factorization with applications in recursive digital filtering,” IEEE Trans. Acoustics, Speech, Signal Processing, vol. ASSP-24, pp. 115–128, Apr. 1976.
31. A. Habibi, “Two-dimensional Bayesian estimate of images,” Proc. IEEE, vol. 60, pp. 878–883, July 1972.
32. R. Chellappa, “Two-dimensional discrete Gaussian Markov random field models for image processing,” in Progress in Pattern Recognition 2, L. N. Kanal and A. Rosenfeld, Eds. Dordrecht, The Netherlands: Elsevier Science Publishers, 1985.
33. R. L. Kashyap, “Image models,” in Handbook of Pattern Recognition and Image Processing, T. Y. Young and K. S. Fu, Eds. Orlando, FL: Academic Press, 1986.
34. J. W. Woods, “Two-dimensional discrete Markovian fields,” IEEE Trans. Inform. Th., vol. IT-18, pp. 232–240, Mar. 1972.
35. B. R. Hunt, “Digital image processing,” Proc. IEEE, vol. 63, pp. 693–708, Apr. 1975.
36. T. S. Huang, W. F. Schreiber, and O. J. Tretiak, “Image processing,” Proc. IEEE, vol. 59, pp. 1586–1609, Nov. 1971.
37. M. Potmesil and I. Chakravarty, “Synthetic image generation with a lens and aperture camera model,” A CM Trans. Graph., vol. 1, pp. 25–108, Apr. 1982.
38. P. A. Stokseth, “Properties of a defocussed optical system,” J. Opt. Soc. Am., vol. 59, pp. 1314–1321, Oct. 1969.
39. J. W. Goodman, Introduction to Fourier Optics. New York: McGraw-Hill, 1968.
40. H. H. Hopkins, “The frequency response of a defocussed optical system,” Proc. Roy. Soc. Ser. A, vol. 231, pp. 91–103, Feb. 1955.
41. J. Bescos, I. Glaser, and A. A. Sawchuk, “Restoration of color images degraded by chromatic aberrations,” Applied Optics, vol. 19, pp. 3869–3876, Nov. 1980.
42. A. M. Tekalp, H. Kaufman, and J. W. Woods, “Identification of image and blur parameters for the restoration of noncausal blurs,” IEEE Trans. Acoustics, Speech, Signal Processing, vol. ASSP-34, pp. 963–972, Aug. 1986.
43. J. Biemond, F. C. van der Putten, and J. W. Woods, “Identification and restoration of images with symmetric noncausal blurs,” IEEE Trans. Circ. Syst., vol. CAS-35, 385–393, Apr. 1988.
44. T. G. Stockham, Jr., T. M. Cannon, and R. B. Ingebretsen, “Blind deconvolution through digital signal processing,” Proc. IEEE, vol. 63, pp. 678–692, Apr. 1975.
45. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing, ch. 10. Englewood Cliffs, NJ: Prentice-Hall, 1974.
46. L. Ljung and T. Söderström, Theory and Practice of Recursive Identification. Cambridge, MA: M.I.T. Press, 1983.
47. D. Graupe, D. J. Krause, and J. B. Moore, “Identification of autoregressive moving average parameters of time series,” IEEE Trans. Automatic Control, pp. 104–106, Feb. 1975.
48. A. Rosenfeld and A. Kak, Digital Picture Processing, 2nd ed. New York: Academic Press, 1982.
49. K. A. Dines and A. C. Kak, “Constrained least-squares filtering,” IEEE Trans. Acoustics, Speech, Signal Processing, vol. ASSP-25, pp. 346–350, Aug. 1977.
50. J. Biemond, J. Rieske, and J. J. Gerbrands, “A fast Kalman filter for images degraded by both blur and noise,” IEEE Trans. Acoustics, Speech, Signal Processing, vol. ASSP-31, pp. 1248– 1256, Oct. 1983.
51. P. H. Van Cittert, “Zum Einfluss der Spaltbreit auf die Intensitatsverteilung in Spektrallinien II,” Z. Physik, vol. 69, pp. 298–308, 1931.
52. H. Bially, “Iterative Behandlung linearer Funktionalgleichungen,” Arch. Ration. Mech. Anal., vol. 4, pp. 166–176, July 1959.
53. L. Landweber, “An Iteration formula for Fredholm integral equations of the first kind,” Am. J. Math.,vol. 73, pp. 615–624, 1951.
54. O. N. Strand, “Theory and methods related to the singular-function expansion and Landweber's iteration for integral equations of the first kind,” Siam J. Numer. Anal., vol. 11, pp. 798–825, Sept. 1974.
55. D. G. Luenberger, Introduction to Linear and Nonlinear Programming. Reading, MA: Addison-Wesley, 1973.
56. R. Fletcher, Practical Methods of Optimization, Vol. 1: Unconstrained Optimization. Chichester: Wiley, 1980.
57. M. Z. Nashed, “Operator theoretic and computational approaches to ill-posed problems with applications to antenna theory,” IEEE Trans. Antennas Propagat., vol. AP-29, pp. 220–231, Mar. 1981.
58. J. B. Abbiss, C. DeMol, and H. S. Dhadwal, “Regularized iterative and non-iterative procedures for object restoration from experimental data,” Optica Acta, vol. 30, pp. 107–124, Nov. 1983.
59. E. R. Pike, J. C. McWhirter, M. Bertero, and C. DeMol, “Generalized information theory for inverse problems in signal processing,” Proc. Inst. Elec. Eng., Pt. F, vol. 131, pp. 660–667, Oct. 1984.
60. M. Bertero, C. DeMol, and G. A. Viano, “On the regularization of linear inverse problems in Fourier optics,” in Applied Inverse Problems, P. C. Sabatier, Ed., vol. 85. Berlin: Springer-Verlag, 1978.
61. A. Lannes, S. Roques, and M. J. Casonove, “Resolution and robustness in image processing: a new regularization principle,”. Opt. Soc. Amer., vol. 4, pp. 189–199, Jan. 1987.
62. N. B. Karayiannes and A. N. Venetsanopoulos, “Image restoration: a regularization approach,” Proc. 2nd Int. Conf. on Image Processing and its Applications, 1986, pp. 1–5.
63. H. Stark, Ed., Image Recovery: Theory and Application. Orlando: Academic Press, 1987.
64. M. Z. Nashed, “Aspects of generalized inverses in analysis and regularization,” in Generalized Inverses and Applications. New York: Academic Press, pp. 193–244, 1976.
65. M. Z. Nashed, Ed., III-posed Problems: Theory and Practice. Dordrecht: Reidel, 1981.
66. J. Hadamard, Lectures on the Cauchy Problem in Linear Partial Differential Equations. New Haven: Yale University Press, 1923.
67. D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind,” J. Ass. Comput. Mach., vol. 9, pp. 84–97, 1962.
68. S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by inversion of the linear systems produced by quadrature,”J. Ass. Comput. Mach.,vol. 10, pp. 97–101, 1963.
69. S. F. Gull and J. Skilling, “Maximum entropy method in image processing,” Proc. Inst. Elec. Eng. F., vol. 131, pp. 646–659, Oct. 1984.
70. C. AuYeung, R. M. Mersereau, and R. W. Schafer, “Maximum entropy deconvolution,” Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, 1986, pp. 273–276.
71. G. Wahba, “Practical approximate solutions to linear operator equations when the data are noisy,” SIAMJ. Math. Anal., vol. 14, pp. 651–667, Sept. 1977.
72. D. Girard, “Practical optimal regularization of large linear systems,” Mathematical Modeling and Numerical Analysis, vol. 20, pp. 75–87, 1986.
73. A. K. Katsaggelos, J. Biemond, R. M. Mersereau, and R. W. Schafer, “A general formulation of constrained iterative restoration algorithms,” Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, 1985, pp. 700–703.
74. J. F. Abramatic and L. M. Silverman, “Nonlinear restoration of noisy images,” IEEE Trans. Patt. Anal. Mach. Int., vol. PAMI-4, pp. 141–149, Mar. 1982.
75. H. E. Knutsson, R. Wilson, and G. H. Granlund, “Anisotropic nonstationary image estimation and its applications: Part I— Restoration of noisy images,” IEEE Trans. Commun., vol. COM-31, pp. 388–397, May 1983.
76. K. Stewart and T. S. Duranni, “Constrained signal reconstructin—a unified approach,” Signal Processing III: Theories and Applications, I. T. Young et al. Eds. Amsterdam: Elsevier North Holland, 1986.
77. D. B. Sherman, K. A. Stewart, and T. S. Durrani, “The use of context in image restoration,” Proc. IEEE Int. Conf. Acoustics, Speech, Signal Proces., 1986, pp. 1473–1476.
78. H. J. Trussell and M. R. Civanlar, “The initial estimate in constrained iterative restoration,” Proc. IEEE Int. Conf. on Acoustics, Speech, Signal Proc., Feb. 1983, pp. 643–646.
79. L. M. Bregman, “The method of successive projection for finding a common point of convex sets,” Soviet Math. Dok-lady, vol. 6, pp. 688–692, 1965.
80. M. R. Civanlar and H. J. Trussell, “Digital image restoration using fuzzy sets,” IEEE Trans. Acoustics, Speech, Signal Processing, vol. ASSP-34, pp. 919–936, Aug. 1986.
81. R. W. Gerchberg, “Super-resolution through error energy reduction,” Optica Acta, vol. 21, pp. 709–720, 1974.
82. A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circ. Syst., vol. CAS-22, pp. 735–742, Sept. 1975.
83. M. H. Hayes, J. S. Lim, and A. V. Oppenheim, “Signal reconstruction from phase or magnitude,” IEEE Trans. Acoustics, Speech, Signal Processing, vol. ASSP-28, pp. 672–680, Dec. 1980.
84. M. I. Sezan and A.M. Tekalp, “Iterative image restoration with ringing suppression using POCS,” Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, 1988, pp. 1300–1303.
85. G. L. Anderson and A. N. Netravali, “Image restoration based on a subjective criterion,” IEEE Trans. Systems, Man, Cybernetics, vol. SMC-6, pp. 845–853, Dec. 1976.
86. A. M. Tekalp, J. W. Woods, and H. Kaufman, “A multiple model algorithm for the adaptive restoration of images,” Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, 1983, pp. 832– 835.
87. B. R. Hunt, “Bayesian methods in nonlinear digital image restoration,” IEEE Trans. Computers, vol. C-26, pp. 219–229, Mar. 1977.
88. H. J. Trussell and B. R. Hunt, “Improved methods of maximum a posteriori restoration,” IEEE Trans. Computers, vol. C-27, pp. 57–62, Jan. 1979.
89. R. Marucci, R. M. Mersereau, and R. W. Schafer, “Constrained iterative deconvolution using a conjugate gradient algorithm,” Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, 1982, pp. 1845–1848.
90. R. Prostand R. Goutte, “Discrete constrained iterative deconvolution with optimized rate of convergence,” Signal Processing, vol. 7, pp. 209–230, Dec. 1984.
91. C. L. Yeh and R. T. Chin, “Constrained optimization for image restoration using nonlinear programming,” Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, 1985, pp. 676– 679.
92. T. K. Sarkar, F. I. Tseng, S. A. Dianat, and B. Z. Hollmann, “Deconvolution by the conjugate gradient method,” Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, Mar. 1985, pp. 445–488.
93. S. Singh, S. N. Tandon, and H. M. Gupta, “An iterative restoration technique,” Signal Processing, vol. 11, pp. 1–11, July 1986.
94. C. E. Morris, M. A. Richards, and M. H. Hayes, “Iterative deconvolution algorithm with quadratic convergence,” J. Opt. Soc. Amer. A, vol. 4, pp. 200–207, 1987.
95. C. E. Morris, M. A. Richards, and M. H. Hayes, “Fast reconstruction of linearly distorted signals,” IEEE Trans. Acoustics, Speech, Signal Processing, vol. ASSP-36, pp. 1017–1025, July 1988.
96. R. L. Lagendijk, R. M. Mersereau, and J. Biemond, “On increasing the convergence rate of regularized iterative image restoration algorithms,” Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, 1987, pp. 1183–1186.
97. R. L. Lagendijk, D. L. Angwin, H. Kaufman, and J. Biemond, “Recursive and iterative methods for image identification and restoration,” Proc. 4th European Signal Processing Conf. EUSIPCO-88, pp. 235–238.
98. R. L. Lagendijk, J. Biemond, and D. E. Boekee, “Blur identification using the expectation-maximization algorithm,” Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, 1989, pp. 1397–1400.
99. R.C. Gonzalez and P. Wintz, Digital Image Processing. Reading, MA: Addison-Wesley, 1987.