The Papoulis-Gerchberg Algorithm with Unknown Signal Bandwidth

  • Manuel Marques
  • Alexandre Neves
  • Jorge S. Marques
  • João Sanches
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4141)


The Papoulis-Gerchberg algorithm has been extensively used to solve the missing data problem in band-limited signals. The interpolation of low-pass signals with this algorithm can be done if the signal bandwidth is known. In practice, the signal bandwidth is unknown and has to be estimated by the user, preventing an automatic application of the Papoulis-Gerchberg algorithm. In this paper, we propose a method to automatically find this parameter, avoiding the need of the user intervention during the reconstruction process. Experimental results are presented to illustrate the performance of the proposed algorithm.


Discrete Fourier Transform Original Signal Lena Image Signal Bandwidth Estimate Image 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Papoulis, A.: A new algorithm in spectral analysis and band-limited extrapolation. IEEE Transactions on Circuits Syst. 19, 735–742 (1975)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Papoulis, A.: A new method in image restoration. In: JSTAC, Paper VI-3 (1973)Google Scholar
  3. 3.
    Gerchberg, R.W.: Super-resolution through error energy reduction. Optica Acta 21-9, 709–720 (1974)Google Scholar
  4. 4.
    Wingham, D.J.: The reconstruction of a band-limited function and its Fourier transform from a finite number of samples at arbitrary locations by singular value decomposition. IEEE Transactions on Circuit Theory 40, 559–570 (1992)Google Scholar
  5. 5.
    Yen, J.L.: On nonuniform sampling of bandwidth-limited signals. IRE Transactions on Circuit Theory CT-3, 251–259 (1956)CrossRefGoogle Scholar
  6. 6.
    Thomas, J.O., Yao, K.: On some stability and interpolatory properties of nonuniform sampling expansions. IEEE Transactions on Circuit Theory 14, 404–408 (1967)CrossRefGoogle Scholar
  7. 7.
    Benedetto, J., Chui, C.K. (eds.): Irregular sampling and frames. In: Wavelets: A Tutorial in Theory and Applications, pp. 445–507. Academic Press, London (1992)Google Scholar
  8. 8.
    Feichtinger, H.G., Gröchenig, K., Strohmer, T.: Efficient numerical methods in non-uniform sampling theory. Numerische Mathematik 69, 423–440 (1995)CrossRefMathSciNetMATHGoogle Scholar
  9. 9.
    Ferreira, P.J., Marvasti, F.A. (eds.): Iterative and Noninterative Recovery of Missing Samples for 1-D Band-Limited Signals. In: Sampling Theory and Practice, pp. 235–282. Plenum Publishing Corporation (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Manuel Marques
    • 1
  • Alexandre Neves
    • 1
  • Jorge S. Marques
    • 1
  • João Sanches
    • 1
  1. 1.Instituto Superior Técnico & Instituto de Sistemas e RobóticaLisboaPortugal

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