OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 5, Iss. 8 — Aug. 1, 1988
  • pp: 1193–1200

Convolution-based framework for signal recovery and applications

A. Enis Çetin and Rashid Ansari  »View Author Affiliations


JOSA A, Vol. 5, Issue 8, pp. 1193-1200 (1988)
http://dx.doi.org/10.1364/JOSAA.5.001193


View Full Text Article

Enhanced HTML    Acrobat PDF (933 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The method of projections on convex sets is a procedure for signal recovery when partial information about the signal is available in the form of suitable constraints. We consider the use of this method in an inner-product space in which the vector space consists of real sequences and vector addition is defined in terms of the convolution operation. Signals with a prescribed Fourier-transform magnitude constitute a closed and convex set in this vector space, a condition that is not valid in the commonly used l2 (or L2) Hilbert-space framework. This new framework enables us to construct minimum-phase signals from the partial Fourier-transform magnitude and/or phase information.

© 1988 Optical Society of America

History
Original Manuscript: May 5, 1986
Manuscript Accepted: April 21, 1988
Published: August 1, 1988

Citation
A. Enis Çetin and Rashid Ansari, "Convolution-based framework for signal recovery and applications," J. Opt. Soc. Am. A 5, 1193-1200 (1988)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-5-8-1193


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. C. Youla, H. Webb, “Image restoration by the method of convex projections. Part 1. Theory,”IEEE Trans. Med. Imag. MI-1, 81–94 (1982). [CrossRef]
  2. L. B. Bregman, “The method of successive projection for finding a common point of convex sets,” Dokl. USSR 162, 688–692 (1965).
  3. A. Lent, H. Tuy, “An iterative algorithm for extrapolation of band limited functions,”J. Math. Anal. Appl. 83, 554–565 (1981). [CrossRef]
  4. M. I. Sezan, H. Stark, “Image restoration by the method of convex projections. Part 2. Applications and numerical results,”IEEE Trans. Med. Imag. MI-1, 95–101 (1982). [CrossRef]
  5. H. J. Trussell, M. R. Civanlar, “Feasible solution in signal restoration,”IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 201–212 (1984). [CrossRef]
  6. A. E. Cetin, R. Ansari, “An iterative procedure for designing two dimensional FIR filters,” Electron. Lett. 23, 131–134. (1987). [CrossRef]
  7. A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Chap. 10.
  8. B. Bogert, M. Heally, J. W. Tukey, “The quefrency analysis of time series for echoes: cepstrum, pseudo-autocovariance, cross cepstrum,” in Symposium on Time Series Analysis, M. Rosenblatt, ed. (Wiley, New York, 1963), pp. 208–243.
  9. E. Krajnik, B. Pondelicek, “Cepstrum as logarithm in a Banach algebra,” in Proceedings of the European Signal Processing Conference, European Association for Signal Processing, ed. (Elsevier, Amsterdam, 1986), pp. 414–416.
  10. W. Rudin, Functional Analysis (McGraw-Hill, New York, 1973).
  11. T. F. Quatieri, J. M. Tribolet, “Computation of the real cepstrum and minimum-phase reconstruction,” in Programs for Digital Signal Processing, Digital Signal Processing Committee, eds. (Institute of Electrical and Electronics Engineers, New York, 1979), Chap. 7.2.
  12. P. Halmos, Introduction to Hilbert Space (Chelsea, New York, 1957).
  13. C. N. Dorny, A Vector Approach to Models and Optimization (Wiley, New York, 1968).
  14. T. J. Berkhout, “On the minimum phase criterion of sampled signals,”IEEE Trans. Geosci. Electron. GE-11, 186–196 (1973). [CrossRef]
  15. M. H. Hayes, J. S. Lim, A. V. Oppenheim, “Signal reconstruction from phase or magnitude,”IEEE Trans. Acoust. Speech Signal Process. ASSP-28, 672–680 (1980). [CrossRef]
  16. T. F. Quatieri, A. V. Oppenheim, “Iterative techniques for minimum signal reconstruction from phase or magnitude,”IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1187–1193 (1981). [CrossRef]
  17. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27–29 (1978). [CrossRef] [PubMed]
  18. A. Levi, H. Stark, “Image restoration by the method of generalized projections with applications to restoration from magnitude,” J. Opt. Soc. Am. A 1, 932–943 (1984). [CrossRef]
  19. C. L. Bryne, M. A. Fiddy, “Estimation of continuous object distributions from limited Fourier magnitude measurements,” J. Opt. Soc. Am. A 4, 112–117 (1987). [CrossRef]
  20. D. E. Dudgeon, “The existence of cepstra for two-dimensional polynomials,”IEEE Trans. Acoust. Speech Signal Process. ASSP-23, 115–128 (1975).
  21. D. M. Goodman, “Some properties of the multidimensional complex cepstrum and their relationship to the stability of multidimensional systems,” Circuits Syst. Signal Process. 6, 3–30 (1987). [CrossRef]
  22. M. P. Ekstrom, J. W. Woods, “Two-dimensional spectral factorization with applications in recursive digital filtering,”IEEE Trans. Acoust. Speech Signal Process. ASSP-24, 115–128 (1976). [CrossRef]
  23. M. A. Fiddy, King’s College, London (personal communication, April1986).
  24. A. W. Lohmann, B. Wirnitzer, “Triple correlations,” Proc. IEEE 72, 889–901 (1984). [CrossRef]
  25. A. E. Cetin, R. Ansari, “A procedure for antenna array pattern synthesis,” in Proceedings of the International IEEE Conference on Acoustics, Speech and Signal Processing (Institute of Electrical and Electronics Engineers, New York, 1987), pp. 2308–2311.
  26. D. G. Luenberger, Optimization by Vector Space Methods (Wiley, New York, 1968).

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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited