OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 13, Iss. 3 — Mar. 1, 1996
  • pp: 464–469

Scanning singular-value-decomposition method for restoration of images with space-variant blur

D. A. Fish, J. Grochmalicki, and E. R. Pike  »View Author Affiliations

JOSA A, Vol. 13, Issue 3, pp. 464-469 (1996)

View Full Text Article

Enhanced HTML    Acrobat PDF (4262 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present a method that can efficiently restore large images, blurred possibly nonuniformly and contaminated with noise, by use of a scanning singular-value-decomposition (SVD) method. Such an approach bypasses the prohibitive storage and speed limitations of the SVD method, thus, to our knowledge for the first time, making possible the restoration of reasonably sized images. We make use of the linear and local nature of the point spread function (PSF) to scan the image and restore it in the same raster without incurring blocking effects that are due to the overlap in neighboring reconstruction areas. The increase in speed compared with the conventional SVD approach can be many orders of magnitude, depending on the ratio of the point-spread blur to the image size. For example, if the linear extent of the PSF is one-eighth that of the image, a speed-up factor greater than 106 is achieved. A similar but less accurate solution to the problem of spatially variant blur by use of scanning Fourier transforms, which allows an even faster solution, is also described.

© 1996 Optical Society of America

Original Manuscript: February 7, 1995
Revised Manuscript: September 13, 1995
Manuscript Accepted: August 29, 1995
Published: March 1, 1996

D. A. Fish, J. Grochmalicki, and E. R. Pike, "Scanning singular-value-decomposition method for restoration of images with space-variant blur," J. Opt. Soc. Am. A 13, 464-469 (1996)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Bertero, E. R. Pike, “Signal processing for linear instrumental systems with noise: A general theory with illustrations from optical imaging and light scattering problems,” in Handbook of Statistics 10: Signal Processing and Its Applications, N. K. Bose, C. R. Rao, eds. (North-Holland, Amsterdam, 1993), pp. 1–46.
  2. A. N. Tikhonov, N. Y Arsenin, Solutions of Ill-posed Problems (Winston/Wiley, Washington, 1977).
  3. M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging: A singular value analysis I—The case of coherent illumination,” Opt. Acta 29, 727–746 (1982). [CrossRef]
  4. M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction limited imaging: A singular value analysis II—The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982). [CrossRef]
  5. L. Landweber, “An iterative formula for Fredholm integral equations of the first kind,” Amer. J. Math. 73, 615–624 (1951). [CrossRef]
  6. M. Bertero, F. Maggio, E. R. Pike, D. A. Fish, “Assessment of methods used for reconstructing HST images,” in The Restoration of HST Images and Spectra II, R. Hamish, R. L. White, eds. (NASA, Space Telescope Science Institute, Baltimore, Md., 1994), pp. 300–307.
  7. W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62, 55–59 (1972). [CrossRef]
  8. L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745–754 (1974). [CrossRef]
  9. A. A. Sawchuk, “Space-variant restoration by co-ordinate transformation,” J. Opt. Soc. Am. 64, 138–144 (1974). [CrossRef]
  10. S. Rathee, Z. J. Koles, T. R. Overton, “Image restoration in computed tomography—Restoration of experimental CT images,” IEEE Trans. Med. Imag. 11, 546–553 (1992). [CrossRef]
  11. H. J. Trussell, S. Fogel, “Identification and restoration of spatially variant motion blurs in sequential images,” IEEE Trans. Imag. Proc. 1, 123–126 (1992). [CrossRef]
  12. A. DeSantis, A. Germani, L. Jetto, “Space-variant recursive restoration of noisy images,” IEEE Trans. Circuits Syst. Analog Digital Signal Proc. 41, 249–261 (1994). [CrossRef]
  13. S. J. Reeves, “Optimal space-varying regularization in iterative image restoration,” IEEE Trans. Imag. Proc. 3, 319–324 (1994). [CrossRef]
  14. S. Koch, H. Kaufman, J. Biemond, “Restoration of spatially varying blurred images using multiple model-based extended Kalman filters,” IEEE Trans. Imag. Proc. 4, 520–523 (1995). [CrossRef]
  15. J. B. Abbiss, J. C. Allen, H. J. Whitehouse, “Computational issues in regularized restoration using large imaging operators,” Titan Spectron Report No. 94-3341-01, ONR Contract No. N00014-93-C-0109 (Tital Spectron Inc., Santa Ana, Calif., 1994).
  16. Lenna Sjoobloom, Playboy centerfold, November1972.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited