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Reviews of topical problems


Image restoration with minimum a priori information


P.K. Shternberg Astronomical Institute at the M.V. Lomonosov Moscow State University, poselok Nauchnyi, Crimea, Russian Federation

A consistent approach to the image restoration problem is presented, wich does not use Bayesian a priori information. Photon noise is taken into account. The unknown object is treated as a multidimensional set of parameters that have to be statistically estimated in an efficient way. The approach is based on an extended notion of feasible estimate (in the sense of information theory) and on Occam’s razor rule of choosing the simplest object which is consistent with the data. Occam’s rule is applied by transformation to principal components of the inverse (or maximum likelihood) estimate, which are generated by Fisher’s information matrix. The same approach can also be applied to various other inverse problems.

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Fulltext is also available at DOI: 10.1070/PU1995v038n02ABEH000068
PACS: 95.75.−z, 95.75.Pq (all)
DOI: 10.1070/PU1995v038n02ABEH000068
URL: https://ufn.ru/en/articles/1995/2/b/
A1995QR33900002
Citation: Terebizh V Yu "Image restoration with minimum a priori information" Phys. Usp. 38 137–167 (1995)
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Оригинал: Теребиж В Ю «Восстановление изображений при минимальной априорной информации» УФН 165 143–176 (1995); DOI: 10.3367/UFNr.0165.199502b.0143

References (129) ↓ Cited by (22) Similar articles (20)

  1. Frieden B R Picture Processing And Digital Filtering (Ed. T S Huang) (Berlin: Springer, 1979) p. 179
  2. Lord Rayleigh (Strutt J W) Scientific Papers Vol. 1 (New York: Dover, 1964)
  3. Schuster A Terrest. Magn. 3 13 (1898)
  4. Schuster A Proc. R. Soc. London 77 136 (1906)
  5. Feynman R P, Leighton R B, Sands M The Feynman Lectures In Physics Vol. 2 (Reading, MA: Addison-Wesley, 1964), Ch. 40; Feinman R, Leiton R, Sends M Feinmanovskie Lektsii Po Fizike (M.: Mir, 1966)
  6. Terebizh V Yu Proc. 3rd ESO/ST-ECF Data Analysis Workshop (ESO Conf. and Workshop Proc., No. 38, Eds P J Grosbol, R H Warmels) (Garching: ESO, 1991)
  7. Shannon C Bell Syst. Techn. J. 27 379 (1948); Shannon C Bell Syst. Techn. J. 27 623 (1948)
  8. Shannon C Proc. IRE 37 10 (1949)
  9. Bayes T "An essay towards solving a problem in the doctrine of chances" (1763); Reprinted in, Bayes T Biometrika 45 293 (1958)
  10. Zacks S The Theory Of Statistical Inference (New York: Wiley, 1971); Zaks S Teoriya Statisticheskikh Vyvodov (M.: Mir, 1975)
  11. Kolmogorov A N Izv. AN SSSR, Ser. Mat. 5 3 (1941)
  12. Wiener N "Extrapolation, interpolation, and smoothing of stationary time series with engineering applications" MIT NDRC Report (1942); Reprinted, Wiener N Extrapolation, Interpolation, And Smoothing Of Stationary Time Series With Engineering Applications (MIT Press, 1949)
  13. Turchin V F, Kozlov V P, Malkevich M S Usp. Fiz. Nauk 102 345 (1970); Turchin V F, Kozlov V P, Malkevich M S Sov. Phys. Usp. 13 681 (1971)
  14. Phillips D L J. Assoc. Comput. Mach. 9 84 (1962)
  15. Twomey S J. Assoc. Comp. Mach. 10 97 (1963)
  16. Twomey S J. Franklin Inst. 279 95 (1965)
  17. Tikhonov A N Dokl. Akad. Nauk SSSR 151 501 (1963)
  18. Tikhonov A N Dokl. Akad. Nauk SSSR 153 49 (1963)
  19. Jaynes E T Phys. Rev. 106 620 (1957)
  20. Jaynes E T Phys. Rev. 108 171 (1957)
  21. Burg J P 37th Ann. Soc. of Expl. Geophys. Meeting (Oklahoma City OK: Stanford Univ. Geophys. Dept., 1967)
  22. Frieden B R J. Opt. Soc. Am. 62 511 (1972)
  23. Veklerov E, Llacer J IEEE Trans. Med. Imaging 6 313 (1987)
  24. Llacer J, Veklerov E IEEE Trans. Med. Imaging 8 186 (1989)
  25. Terebizh V Yu Astrofizika 32 327 (1990); Terebizh V Yu Astrophysics 32 184 (1990)
  26. Terebizh V Yu Astrofizika 33 409 (1990); Terebizh V Yu Astrophysics 33 536 (1990)
  27. Terebizh V Yu Astron. Astrophys. Trans. 1 3 (1991)
  28. Terebizh V Yu Astron. Astrophys. 270 543 (1993)
  29. Terebizh V Yu, Biryukov V V Astron. Astrophys. Trans. 6 (37) (1994)
  30. Terebizh V Yu, Biryukov V V Doklady R A N, v pechati
  31. Terebizh V Yu, Biryukov V V Astrophys. Space Sci. 218 65 (1994)
  32. Mints M Ya, Prilepskii E D Opt. Spektrosk. 75 696 (1993); Mints M Ya, Prilepskii E D Opt. Spectrosc. 75 413 (1993)
  33. Pina R K, Puetter R C Publ. Astron. Soc. Pacific 105 630 (1993)
  34. Helstrom C W J. Opt. Soc. Am. 59 164 (1969)
  35. Helstrom C W J. Opt. Soc. Am. 60 659 (1970)
  36. Mehta C L Progress In Optics Vol. 8 (Ed. E Wolf) (Amsterdam: North-Holland, 1970) p. 373
  37. Troup G G Progress In Quantum Electronics Vol. 2 (Eds J H Sanders, S Stenholm, 1972) p. 1
  38. Terebizh V Yu Analiz Vremennykh Ryadov v Astrofizike (M.: Nauka, 1992)
  39. Cox D R J. R. Statist. Soc. B 17 129 (1955)
  40. Mandel L Proc. Phys. Soc. London 72 1037 (1958)
  41. Mandel L Proc. Phys. Soc. London 74 233 (1959)
  42. Snyder D L, Hammoud A M, White R L J. Opt. Soc. Am. A 10 1014 (1993)
  43. Borovkov A A Matematicheskaya Statistika (M.: Nauka, 1994)
  44. Fisher R A Philos. Trans. A 222 309 (1921)
  45. Toraldo di Francia G J. Opt. Soc. Am. 45 497 (1955)
  46. Seber G A F Linear Regression Analysis (New York: Wiley, 1977); Seber Dzh Lineinyi Regressionnyi Analiz (M.: Mir, 1980)
  47. Ermakov S M, Zhiglyavskii A A Matematicheskaya Teoriya Optimal’nogo Eksperimenta (M.: Nauka, 1987)
  48. Morris J Philos. Mag. 37 (7) 106 (1946)
  49. Bertero M Inverse Problems (Ed. G Talenti) (Berlin: Springer, 1986) p. 52
  50. Booth A D Numerical Methods (London: Butterworths, 1955); But E Chislennye Metody (M.: Fizmatgiz, 1959)
  51. Lanczos C Applied Analysis (New York: Prentice Hall, 1956); Lantsosh K Prakticheskie Metody Prikladnogo Analiza (M.: Fizmatgiz, 1961)
  52. Faddeev D K Trudy MIAN SSSR 53 387 (1959)
  53. Faddeev D K, Faddeeva V N Zhurn. Vychisl. Matem. Matem. Fiz. 1 412 (1961)
  54. Bard Y Nonlinear Parameter Estimation (New York: Academic Press, 1974); Bard I Nelineinoe Otsenivanie Parametrov (M.: Statistika, 1979)
  55. Fisher R A Philos. Trans. R. Soc. London A 222 309 (1922)
  56. Fisher R A Messenger Of Mathematics 41 150 (1912)
  57. Aitken A C, Silverstone H Proc. R. Soc. Edinburgh A 61 186 (1942)
  58. Frechet M Rev. Inst. Int. Stat. 18 2 (1943)
  59. Darmois G Rev. Inst. Int. Stat. B 9 (1945)
  60. Rao C R Bull. Calcutta Math. Soc. 37 81 (1945)
  61. Cramer H Mathematical Methods Of Statistics (New York: Princeton University Press, 1946); Kramer G Matematicheskie Metody Statistiki (M.: Mir, 1975)
  62. Hoerl A E, Kennard R W Technometrics 12 55 (1970)
  63. Hoerl A E, Kennard R W Technometrics 12 69 (1970)
  64. Edgeworth E Y J. R. Stat. Soc. 71 381 499 651 (1908)
  65. Edgeworth E Y J. R. Stat. Soc. 72 81 (1909)
  66. Wiener N Cybernetics (New York: M.I.T. Press and Wiley, 1961); Viner N Kibernetika (M.: Nauka, 1983)
  67. Cox D R, Hinkley D V Theoretical Statistics (New York: Chapman and Hall, 1974); Koks D, Khinkli D Teoreticheskaya Statistika (M.: Mir, 1978)
  68. Kullback S, Leibler R A Ann. Math. Stat. 22 79 (1951)
  69. Kendall M G, Stuart A The Advanced Theory Of Statistics Vol. 2, 3 (London: Griffin, 1969); Kendall M, Styuart A Statisticheskie Vyvody i Svyazi (M.: Nauka, 1973)
  70. Bol’shev L N, Smirnov N V Tablitsy Matematicheskoi Statistiki (M.: Nauka, 1965)
  71. Kolmogorov A N Problemy Peredachi Informatsii 1 3 (1965)
  72. Kolmogorov A N Problemy Peredachi Informatsii 5 3 (1969)
  73. Von Mises R Wahrscheindlichkeit, Statistik Und Wahrheit (Berlin: Springer, 1928)
  74. Solomonoff R Inform. Control 7 1 (1964)
  75. Martin-Lof P Inform. Control 9 602 (1966)
  76. Zvonkin A K, Levin L A Usp. Matem. Nauk 25 (6) 85 (1970)
  77. Ford J Phys. Today 36 40 (1983)
  78. Rose A Vision: Human And Electronic (New York: Plenum Press, 1973); Rouz A Zrenie Cheloveka i Elektronnoe Zrenie (M.: Mir, 1977)
  79. Bershad N J J. Opt. Soc. Am. 59 157 (1969)
  80. Born M, Wolf E Principles Of Optics (Oxford: Pergamon Press, 1964); Born M, Vol’f E Osnovy Optiki (M.: Nauka, 1970)
  81. Davenport W B, Root W L An Introduction To The Theory Of Random Signals And Noise (New York: McGraw-Hill, 1958); Davenport V, Rut V Vvedenie v Teoriyu Sluchainykh Signalov i Shumov (M.: IL, 1960)
  82. Cole E R PhD Dissertation (Salt Lake City: Dept. of Electrical Eng., Univ. o f Utah, 1973)
  83. Pinsker M S Dokl. Akad. Nauk SSSR 99 213 (1956)
  84. Fellgett P B, Linfoot E H Philos. Trans. R. Soc. London A 247 369 (1955)
  85. Gel’fand I M, Yaglom A M Usp. Mat. Nauk 12 3 (1957)
  86. Terebizh V Yu Astrofizika, v pechati
  87. Airy G B Trans. Cambr. Philos. Soc. 5 283 (1835)
  88. O’Neill E L J. Opt. Soc. Am. 46 285 1096 (1956)
  89. O’Neill E L Introduction To Statistical Optics (Reading, MA: Addison-Wesley, 1963); O’Neil E Vvedenie v Statisticheskuyu Optiku (M.: Mir, 1966)
  90. Hotelling H J. Educ. Psych. 24 417 498 (1933)
  91. Einstein A, Infeld L The Evolution Of Physics (New York: Simon and Schuster, 1942); Einshtein A Sobranie Nauchnykh Trudov Vol. 4 (M.: Nauka, 1967) p. 357
  92. Kramer H P, Mathews M V IRE Trans. Inf. Theory 2 41 (1956)
  93. Rao C R Sankhya A 26 329 (1964)
  94. Rao C R Linear Statistical Inference And Its Applications (New York: Wiley, 1965); Rao S Lineinye Statisticheskie Metody i Ikh Primeneniya (M.: Nauka, 1968)
  95. Brillinger D R Time Series Analysis (New York: Holt, Rinehart and Winston, 1975); Brillindzher D Vremennye Ryady (M.: Mir, 1980)
  96. Biraud Y Astron. Astrophys. 1 124 (1969)
  97. Bertsekas D P Constrained Optimization And Lagrange Multiplier Methods (New York: Academic Press, 1982); Bertsekas D Uslovnaya Optimizatsiya i Metody Mnozhitelei Lagranzha (M.: Radio i svyaz’, 1987)
  98. Aivazyan S A i dr. Prikladnaya Statistika. Klassifikatsiya i Snizhenie Razmernosti (M.: Finansy i statistika, 1989)
  99. Autonne L Ann. Univ. Lion. 38 1 (1915)
  100. Lawson C L, Hanson R J Solving Least Squares Problems (Englewood Cliffs, NJ: Prentice-Hall, 1974); Louson Ch, Khenson R Chislennoe Reshenie Zadach Metodom Naimen’shikh Kvadratov (M.: Nauka, 1986)
  101. Press W H et al. Numerical Recipes (London: Cambridge Univ. Press, 1986)
  102. Loeve M Probability Theory (New York: Van Nostrand, 1963); Loev M Teoriya Veroyatnostei (M.: IL, 1962)
  103. Jain A K Fundamentals Of Digital Image Processing (Englewood Cliffs, NJ: Prentice-Hall, 1989)
  104. Andrews H C, Patterson C L Am. Math. Mon. 1 1 (1975)
  105. Andrews H C, Patterson C L IEEE Trans. Comput. C 25 140 (1976)
  106. Huang T S, Narendra P M Appl. Opt. 14 2213 (1975)
  107. Andrews H C, Patterson C L IEEE Trans. Acoust. Speech Signal Process. 24 26 (1976)
  108. Pratt W K Digital Image Processing (New York: Wiley, 1978); Prett U Tsifrovaya Obrabotka Izobrazhenii (M.: Mir, 1982)
  109. Schelkunoff S A Bell Syst. Tech. J. 22 80 (1943)
  110. Gorelik G S Dokl. Akad. Nauk SSSR 83 549 (1952)
  111. Toraldo di Francia G J. Opt. Soc. Am. 59 799 (1969)
  112. Rautian S G Usp. Fiz. Nauk 66 475 (1958); Rautian S G Sov. Phys. Usp. 1 245 (1958)
  113. Wolter H Progress In Optics Vol. 1 (Ed. E Wolf) (Amsterdam: North-Holland, 1961) p. 155
  114. Kozlov V P Opt. Spektrosk. 16 501 (1964); Kozlov V P Opt. Spectrosc. 16 271 (1964)
  115. Harris J L J. Opt. Soc. Am. 54 606 (1964)
  116. Harris J L J. Opt. Soc. Am. 54 931 (1964)
  117. Frieden B R J. Opt. Soc. Am. 57 1013 (1967)
  118. Rushforth C K, Harris R W J. Opt. Soc. Am. 58 539 (1968)
  119. Snyder D L, Miller M I Random Point Processes In Time And Space (Berlin: Springer, 1991)
  120. Terebizh V Yu, Cheburnina O K Astron. Astrophys. Trans., in press
  121. Lucy L Astron. J. 104 1260 (1992)
  122. Kolmogorov A N, Tikhomirov V M Usp. Mat. Nauk 14 (2) 3 (1959)
  123. Kotel’nikov V A Materialy k I Vsesoyuz. S’’ezdu Po Vopr. Tekhn. Rekonstr. Dela Svyazi i Razv. Slabotochnoi Prom. (M., 1933)
  124. Snyder D L, Miller M I IEEE Trans. Nucl. Sci. 32 3864 (1985)
  125. Snyder D L et al. IEEE Trans. Med. Imaging 6 228 (1987)
  126. Snyder D L The Restoration of HST Images and Spectra, Proc. of Workshop STSc I (Eds R L White, R J Allen) (Baltimore: NASA, 1990) p. 56
  127. Terebizh V Yu Astron. Astrophys. Trans. 3 251 (1993)
  128. Nicolis J S Dynamics Of Hierarchical Systems. An Evolutionary Approach (Berlin: Springer, 1986); Nikolis Dzh Dinamika Ierarkhicheskikh Sistem (M.: Mir, 1989)
  129. Terebizh V Yu, Cherbunina O K, Cherbunin Yu G Astrofizika 34 419 (1991); Terebizh V Yu, Cheburnina O K, Cheburnin Yu G Astrophysics 34 226 (1991)
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