Advertisement

Recursive total least squares algorithm for image reconstruction from noisy, undersampled frames

  • N. K. Bose
  • H. C. Kim
  • H. M. Valenzuela
Article

Abstract

It is shown how the efficient recursive total least squares algorithm recently developed by C.E. Davila [3] for real data can be applied to image reconstruction from noisy, undersampled multiframes when the displacement of each frame relative to a reference frame is not accurately known. To do this, the complex-valued image data in the wavenumber domain is transformed into an equivalent real data problem to which Davila's algorithm is successfully applied. Two detailed illustrative examples are provided in support of the procedure. Similar reconstruction in the presence of blur as well as noise is currently under investigation.

Key Words

image reconstruction recursive total least squares algorithm image sequence multiple frames interpolation filtering 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S.P. Kim, N.K. Bose, and H.M. Valenzuela, “Recursive Reconstruction of High Resolution Image from Noisy Undersampled Frames,”IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 38, 1013–1027, 1990.Google Scholar
  2. 2.
    S. Van Huffel and J. Vandewalle,The Total Least Squares Problem: Computational Aspects and Analysis, Philadelphia: SIAM, 1991.Google Scholar
  3. 3.
    C.E. Davila, “Recursive Total Least Squares Algorithms for Adaptive Filtering,” inIEEE Proc. Int. Conf. Acoustics, Speech, and Signal Processing (ICASSP), Toronto, Canada, pp. 1853–1856, 1991. Additional details in C.E. Davila, “An Efficient Recursive Total Least Squares Algorithms for FIR Adaptive Filtering,” submitted toIEEE Transaction on Signal Processing, and provided by the author to N.K. Bose.Google Scholar
  4. 4.
    G.H. Golub, “Some Modified Matrix Eigenvalue Problems,”SIAM Rev., vol. 15, 1973, pp. 318–334.Google Scholar
  5. 5.
    I. Schavitt, C.F. Bender, A. Pipano, and R.P. Hosteny, “The Iterative Calculation of Several of the Lowest or Highest Eigenvalues and Corresponding Eigenvectors of Very Large Symmetric Matrices,”Journal of Computational Physics, vol. 11, 1973, pp. 90–108.Google Scholar
  6. 6.
    C.C. Kuo and B.C. Levy, “Discretization and Solution of Elliptic PDE's—A Digital Signal Processing Approach,”Proceedings of IEEE, vol. 78, 1990, pp. 1808–1842.Google Scholar
  7. 7.
    G.H. Golub and C.F. Van Loan,Matrix Computations, Baltimore: The Johns Hopkins University Press, 1983.Google Scholar
  8. 8.
    A.M. Tekalp, M.K. Ozkan, and M.I. Sezan, “High-Resolution Image Reconstruction from Lower-Resolution Image Sequences and Space-Varying Restoration,” inIEEE Proc. Int. Conf. Acoustics, Speech, and Signal Processing (ICASSP), San Francisco, CA, pp. III:169–172, 1992.Google Scholar
  9. 9.
    S.P. Kim and W.Y. Su, “Recursive High-Resolution Reconstruction of Blurred Multiframe Images,” inIEEE Proc. Int. Conf. Acoustics, Speech, and Signal Processing (ICASSP), Toronto, Canada, pp. 2977–2980, 1991.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • N. K. Bose
    • 1
  • H. C. Kim
    • 1
  • H. M. Valenzuela
    • 1
  1. 1.Department of Electrical and Computer Engineering, The Spatial and Temporal Signal Processing CenterThe Pennsylvania State UniversityUniversity Park

Personalised recommendations