OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 9 — Sep. 1, 2001
  • pp: 2079–2088

Recovery of limited-extent images aliased because of spectral undersampling

Philip J. Bones, Nawar Alwesh, T. John Connolly, and Nicholas D. Blakeley  »View Author Affiliations

JOSA A, Vol. 18, Issue 9, pp. 2079-2088 (2001)

View Full Text Article

Enhanced HTML    Acrobat PDF (380 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In imaging situations where observations are made in spatial-frequency space, it is often desirable to lower the number of observations to fewer than that imposed by the Nyquist criterion. It is shown that patterns of regular spectral undersampling lead to aliasing that can be partially eliminated from some regions of a limited-extent image. An algorithm is presented for determining which regions are recoverable and which are not for a given pattern. Noniterative recovery, analogous to that proposed by WalshNielsen-Delaney [J. Opt. Soc. Am. A 11, 572 (1994)], is shown to be feasible in cases of regular undersampling. The work has particular relevance to magnetic resonance imaging and aperture synthesis telescopy.

© 2001 Optical Society of America

OCIS Codes
(100.3020) Image processing : Image reconstruction-restoration
(100.6640) Image processing : Superresolution
(100.6950) Image processing : Tomographic image processing
(110.6960) Imaging systems : Tomography

Original Manuscript: December 11, 2000
Revised Manuscript: February 26, 2001
Manuscript Accepted: February 26, 2001
Published: September 1, 2001

Philip J. Bones, Nawar Alwesh, T. John Connolly, and Nicholas D. Blakeley, "Recovery of limited-extent images aliased because of spectral undersampling," J. Opt. Soc. Am. A 18, 2079-2088 (2001)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. B. R. Hunt, “Super-resolution of images: algorithms, principles, performance,” Int. J. Imaging Syst. Technol. 6, 297–304 (1995). [CrossRef]
  2. Z. P. Liang, P. C. Lauterbur, Principles of Magnetic Resonance Imaging: A Signal Processing Perspective (Institute of Electrical and Electronics Engineers, New York, 1999).
  3. W. N. Brouw, “Aperture synthesis,” Methods Comput. Phys. 14, 131–175 (1975).
  4. R. N. Bracewell, R. S. Colvin, L. R. D’Addario, C. J. Grebenkemper, K. M. Price, A. R. Thompson, “The Stanford five-element radio telescope,” Proc. IEEE 61, 1249–1257 (1973). [CrossRef]
  5. R. J. Marks, “Multidimensional-signal sample dependency at Nyquist densities,” J. Opt. Soc. Am. A 3, 268–273 (1986). [CrossRef]
  6. K. F. Cheung, R. J. Marks, “Imaging sampling below the Nyquist density without aliasing,” J. Opt. Soc. Am. A 7, 92–105 (1990). [CrossRef]
  7. S. J. Reeves, L. P. Heck, “Selection of observations in signal reconstruction,” IEEE Trans. Signal Process. 43, 788–791 (1995). [CrossRef]
  8. D. O. Walsh, P. A. Nielsen-Delaney, “Direct method for superresolution,” J. Opt. Soc. Am. A 11, 572–579 (1994). [CrossRef]
  9. R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 21, 709–720 (1974). [CrossRef]
  10. A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Syst. 22, 735–742 (1975). [CrossRef]
  11. T. J. Connolly, K. A. Landman, L. R. White, “On Gerchberg’s method for the Fourier inverse problem,” J. Aust. Math. Soc. B Appl. Math. 37, 26–44 (1995). [CrossRef]
  12. D. C. Youla, “Generalized image restoration by the method of alternating orthogonal projections,” IEEE Trans. Circuits Syst. 25, 694–702 (1978). [CrossRef]
  13. H. Stark, Image Recovery, Theory and Application (Academic, Orlando, Fla., 1987).
  14. G. Strang, Linear Algebra and Its Applications, 3rd ed. (Harcourt Brace Jovanovitch, San Diego, Calif., 1988).
  15. B. J. Sullivan, B. Liu, “On the use of singular value decomposition and decimation in discrete-time band-limited signal extrapolation,” IEEE Trans. Acoust., Speech, Signal Process. ASSP-32, 1201–1212 (1984). [CrossRef]
  16. D. G. Luenberger, Linear and Nonlinear Programming, 2nd ed. (Addition-Wesley, Reading, Mass., 1984).
  17. J. F. Debatin, G. C. McKinnon, Ultrafast MRI: Techniques and Applications (Springer-Verlag, New York, 1998).
  18. J. J. Benedetto, H. Wu, “A multidimensional irregular sampling algorithm and applications,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 2039–2042.
  19. R. K. S. Kwan, A. C. Evans, G. B. Pike, “An extensible MRI simulator for post-processing evaluation,” Lect. Notes Comput. Sci. 1131, 135–140 (1996) (see also http://www.bic.mni.mcgill.ca/brainweb/ ). [CrossRef]

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 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited