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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 17, Iss. 4 — Feb. 15, 1978
  • pp: 660–666

Image restoration by spline functions

M. J. Peyrovian and A. A. Sawchuk  »View Author Affiliations


Applied Optics, Vol. 17, Issue 4, pp. 660-666 (1978)
http://dx.doi.org/10.1364/AO.17.000660


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Abstract

Spline functions, because of their highly desirable interpolating and approximating characteristics, are used as a potential alternative to the conventional pulse approximation method in digital image processing. In space-invariant imaging systems, the object and point-spread function are represented by a class of spline functions called B-splines. Exploiting the convolutional property of B-splines, the deterministic part of the degraded image is another B-spline of higher degree. A minimum norm principle leading to pseudoinversion is used for the restoration of space-invariant degradations with underdetermined and overdetermined models. The singular-value-decomposition technique is used to determine the pseudoinverse.

© 1978 Optical Society of America

History
Original Manuscript: April 18, 1977
Published: February 15, 1978

Citation
M. J. Peyrovian and A. A. Sawchuk, "Image restoration by spline functions," Appl. Opt. 17, 660-666 (1978)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-17-4-660


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References

  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  2. T. N. E. Greville, Ed., Theory and Applications of Spline Functions (Academic, New York, 1969).
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  4. C. de Boor, J. Math. Mech. 12, 747 (1963).
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  7. H. B. Curry, I. J. Schoenberg, J. Anal. Math. 17, 71 (1966). [CrossRef]
  8. W. K. Pratt, Digital Image Processing (Wiley, New York, 1978), Chap. 9.
  9. H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977), Chap. 7.
  10. M. J. Peyrovian, A. A. Sawchuk, University of Southern California Image Processing Institute Technical Report 620 (1975), p. 86.
  11. A. Albert, Regression and the Moore-Penrose Pseudoinverse (Academic, New York, 1972).
  12. E. D. Nering, Linear Algebra and Matrix Theory (Wiley, New York, 1970).
  13. G. H. Golub, C. Reinsch, Numer. Math. 14, 403 (1970). [CrossRef]
  14. A. A. Sawchuk, M. J. Peyrovian, J. Opt. Soc. Am. 65, 712 (1975). [CrossRef]

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