Abstract

A method of image restoration for certain systems with space-variant point-spread functions is presented. The technique, called coordinate transformation restoration (CTR), is applicable to a large class of optical degradations, and operates by first transforming the degraded image by a geometrical distortion. Following this, space-invariant inverse filtering or estimation and another transformation are used to complete the process. The CTR technique makes restoration practical for a variety of incoherent systems with motion and aberration degradations by effectively reducing the system dimensionality.

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 18.
  2. A. W. Lohmann and D. P. Paris, J. Opt. Soc. Am. 55, 1007 (1965).
  3. A. A. Sawchuk, J. Opt. Soc. Am. 63, 1052 (1973).
  4. T. S. Huang, W. F. Schreiber, and O. J. Tretiak, Proc. IEEE 59, 1586 (1971); M. M. Sondhi, Proc. IEEE 60, 842 (1972).
  5. J. L. Harris, Sr., J. Opt. Soc. Am. 56, 569 (1966); J. L. Harris, Sr., in Evaluation of Motion Degraded Images, edited by M. Nagel, NASA Tech. Rep. No. SP-193 (U. S. Government Printing Office, Washington, D. C., 1968), p. 131; B. L. McGlamery, J. Opt. Soc. Am. 57, 293 (1967); J. Tsujiuchi, in Progress in Optics II, edited by E. Wolf (North-Holland, Amsterdam, 1963), p. 131; P. F. Mueller and G. O. Reynolds, J. Opt. Soc. Am. 57, 1338 (1967).
  6. C. W. Helstrom, J. Opt. Soc. Am. 57, 297 (1967); J. L. Horner, J. Opt. Soc. Am. 59, 553 (1969); J. L. Horner, Appl. Opt. 9, 167 (1970).
  7. D. Slepian, Bell Syst. Tech. J. 46, 2353 (1967); N. E. Nahi, Proc. IEEE 60, 872 (1972); A. Habibi, Proc. IEEE 60, 878 (1972).
  8. C. L. Rino, J. Opt. Soc. Am. 59, 547 (1969).
  9. A. V. Oppenheim, R. W. Schaefer, and T. G. Stockham, Jr., Proc. IEEE 56, 1264 (1968).
  10. B. R. Frieden, J. Opt. Soc. Am. 58, 1272 (1968).
  11. L. J. Cutrona, in Optical and Electro-Optical Information Processing, edited by J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, and A. Vanderburgh, Jr. (M.I.T. Press Cambridge, Mass., 1965), p. 86.
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  13. E. G. Johnston and A. Rosenfeld, in Picture Processing and Psychopictorics, edited by B. S. Lipkin and A. Rosenfeld (Academic, New York, 1970), p. 217.
  14. A. A. Sawchuk, Proc. IEEE 60, 854 (1972).
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  16. Reference 14, p. 211.
  17. G. M. Robbins, Mass. Inst. Tech. Res. Lab. Electronics Quart. Prog. Rept. 93, 243 (1969).
  18. G. M. Robbins and T. S. Huang, Proc. IEEE 60, 862 (1972).
  19. G. M. Robbins, Patt. Recog. 2, 91 (1970).
  20. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965), p. 254; R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. I (Wiley-Interscience, New York, 1966), p. 103; P. Baudelaire, Proc. IEEE 61, 467 (1972).

Born, M.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, London, 1970), p. 209.

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965), p. 254; R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. I (Wiley-Interscience, New York, 1966), p. 103; P. Baudelaire, Proc. IEEE 61, 467 (1972).

Cutrona, L. J.

L. J. Cutrona, in Optical and Electro-Optical Information Processing, edited by J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, and A. Vanderburgh, Jr. (M.I.T. Press Cambridge, Mass., 1965), p. 86.

Frieden, B. R.

B. R. Frieden, J. Opt. Soc. Am. 58, 1272 (1968).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 18.

Harris, Sr., J. L.

J. L. Harris, Sr., J. Opt. Soc. Am. 56, 569 (1966); J. L. Harris, Sr., in Evaluation of Motion Degraded Images, edited by M. Nagel, NASA Tech. Rep. No. SP-193 (U. S. Government Printing Office, Washington, D. C., 1968), p. 131; B. L. McGlamery, J. Opt. Soc. Am. 57, 293 (1967); J. Tsujiuchi, in Progress in Optics II, edited by E. Wolf (North-Holland, Amsterdam, 1963), p. 131; P. F. Mueller and G. O. Reynolds, J. Opt. Soc. Am. 57, 1338 (1967).

Helstrom, C. W.

C. W. Helstrom, J. Opt. Soc. Am. 57, 297 (1967); J. L. Horner, J. Opt. Soc. Am. 59, 553 (1969); J. L. Horner, Appl. Opt. 9, 167 (1970).

Huang, T. S.

G. M. Robbins and T. S. Huang, Proc. IEEE 60, 862 (1972).

T. S. Huang, W. F. Schreiber, and O. J. Tretiak, Proc. IEEE 59, 1586 (1971); M. M. Sondhi, Proc. IEEE 60, 842 (1972).

Johnston, E. G.

E. G. Johnston and A. Rosenfeld, in Picture Processing and Psychopictorics, edited by B. S. Lipkin and A. Rosenfeld (Academic, New York, 1970), p. 217.

Lohmann, A. W.

A. W. Lohmann and D. P. Paris, J. Opt. Soc. Am. 55, 1007 (1965).

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schaefer, and T. G. Stockham, Jr., Proc. IEEE 56, 1264 (1968).

Paris, D. P.

A. W. Lohmann and D. P. Paris, J. Opt. Soc. Am. 55, 1007 (1965).

Rino, C. L.

C. L. Rino, J. Opt. Soc. Am. 59, 547 (1969).

Robbins, G. M.

G. M. Robbins, Mass. Inst. Tech. Res. Lab. Electronics Quart. Prog. Rept. 93, 243 (1969).

G. M. Robbins, Patt. Recog. 2, 91 (1970).

G. M. Robbins and T. S. Huang, Proc. IEEE 60, 862 (1972).

Rosenfeld, A.

E. G. Johnston and A. Rosenfeld, in Picture Processing and Psychopictorics, edited by B. S. Lipkin and A. Rosenfeld (Academic, New York, 1970), p. 217.

Sawchuk, A. A.

A. A. Sawchuk, Proc. IEEE 60, 854 (1972).

A. A. Sawchuk, J. Opt. Soc. Am. 63, 1052 (1973).

Schaefer, R. W.

A. V. Oppenheim, R. W. Schaefer, and T. G. Stockham, Jr., Proc. IEEE 56, 1264 (1968).

Schreiber, W. F.

T. S. Huang, W. F. Schreiber, and O. J. Tretiak, Proc. IEEE 59, 1586 (1971); M. M. Sondhi, Proc. IEEE 60, 842 (1972).

Slepian, D.

D. Slepian, Bell Syst. Tech. J. 46, 2353 (1967); N. E. Nahi, Proc. IEEE 60, 872 (1972); A. Habibi, Proc. IEEE 60, 878 (1972).

Stockham, Jr., T. G.

A. V. Oppenheim, R. W. Schaefer, and T. G. Stockham, Jr., Proc. IEEE 56, 1264 (1968).

T. G. Stockham, Jr., Proc. IEEE 60, 828 (1972).

Tretiak, O. J.

T. S. Huang, W. F. Schreiber, and O. J. Tretiak, Proc. IEEE 59, 1586 (1971); M. M. Sondhi, Proc. IEEE 60, 842 (1972).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, London, 1970), p. 209.

Other (20)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 18.

A. W. Lohmann and D. P. Paris, J. Opt. Soc. Am. 55, 1007 (1965).

A. A. Sawchuk, J. Opt. Soc. Am. 63, 1052 (1973).

T. S. Huang, W. F. Schreiber, and O. J. Tretiak, Proc. IEEE 59, 1586 (1971); M. M. Sondhi, Proc. IEEE 60, 842 (1972).

J. L. Harris, Sr., J. Opt. Soc. Am. 56, 569 (1966); J. L. Harris, Sr., in Evaluation of Motion Degraded Images, edited by M. Nagel, NASA Tech. Rep. No. SP-193 (U. S. Government Printing Office, Washington, D. C., 1968), p. 131; B. L. McGlamery, J. Opt. Soc. Am. 57, 293 (1967); J. Tsujiuchi, in Progress in Optics II, edited by E. Wolf (North-Holland, Amsterdam, 1963), p. 131; P. F. Mueller and G. O. Reynolds, J. Opt. Soc. Am. 57, 1338 (1967).

C. W. Helstrom, J. Opt. Soc. Am. 57, 297 (1967); J. L. Horner, J. Opt. Soc. Am. 59, 553 (1969); J. L. Horner, Appl. Opt. 9, 167 (1970).

D. Slepian, Bell Syst. Tech. J. 46, 2353 (1967); N. E. Nahi, Proc. IEEE 60, 872 (1972); A. Habibi, Proc. IEEE 60, 878 (1972).

C. L. Rino, J. Opt. Soc. Am. 59, 547 (1969).

A. V. Oppenheim, R. W. Schaefer, and T. G. Stockham, Jr., Proc. IEEE 56, 1264 (1968).

B. R. Frieden, J. Opt. Soc. Am. 58, 1272 (1968).

L. J. Cutrona, in Optical and Electro-Optical Information Processing, edited by J. T. Tippett, D. A. Berkowitz, L. C. Clapp, C. J. Koester, and A. Vanderburgh, Jr. (M.I.T. Press Cambridge, Mass., 1965), p. 86.

T. G. Stockham, Jr., Proc. IEEE 60, 828 (1972).

E. G. Johnston and A. Rosenfeld, in Picture Processing and Psychopictorics, edited by B. S. Lipkin and A. Rosenfeld (Academic, New York, 1970), p. 217.

A. A. Sawchuk, Proc. IEEE 60, 854 (1972).

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, London, 1970), p. 209.

Reference 14, p. 211.

G. M. Robbins, Mass. Inst. Tech. Res. Lab. Electronics Quart. Prog. Rept. 93, 243 (1969).

G. M. Robbins and T. S. Huang, Proc. IEEE 60, 862 (1972).

G. M. Robbins, Patt. Recog. 2, 91 (1970).

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965), p. 254; R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. I (Wiley-Interscience, New York, 1966), p. 103; P. Baudelaire, Proc. IEEE 61, 467 (1972).

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