On a Direct Approach for the Solution of Linear Space-Invariant 2-D Differential Convolution Models

  • F. C. Incertis
Conference paper

Abstract

2-D differential convolution operators in a rectangular discrete domain are modelled as linear differential matrix equations of the form Х(t) = Σ AjX(t)Bi + F(t), where the coefficient matrices Ai ∈ IR(MxM),Bi ∈ IR(NxN) and F(t) ∈ IR(MxN) is a piecewise continuous function matrix of t. Under some periodicity assumptions an analytical solution method is presented making use of the 2-D discrete Fourier transform (DFT). For most general problems an iterative computational method founded in the Peano-Baker series is proposed.

Keywords

Convolution Hunt Deconvolution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andrews, H.C. and B.R. Hunt (1977) Digital Image Restoration, Prentice Hall, Englewood Cliffs, New Jersey.Google Scholar
  2. Berger, R.L. and N. Davids (1965) General computer method analysis of condition and diffusion in biological systems with distributive sources, Rev. Sci. Instr. 36, 88–93.CrossRefGoogle Scholar
  3. Brockett, R.W. (1970) Finite Dimensional Linear Systems, John Wiley ans Sons, New York.MATHGoogle Scholar
  4. Cooley J.W. and J.W. Tuckey (1972) An algorithm for the machine computation of complex Fourier series, IEEE Press, Compiled in Digital Signal Processing, 223–228.Google Scholar
  5. Dunford, N, and J.T. Schwartz (1966) Linear Operators, Part 1 Interscience, New York.MATHGoogle Scholar
  6. Fromm, J.E. (1969) Lectures on large scale finite difference computation of incomprensible fluid flows, Rpt. RJ 617, IBM Research, San Jose, Calif.Google Scholar
  7. Gonzalez, R.G. and P. Wints (1977) Digital Image Processing, Addison Wesley, Advanced Book Program, New York.Google Scholar
  8. Goodman, Y.W. (1968) Introduction to Furier Optics, Mac GrawHill, New York.Google Scholar
  9. Greenspan, D. (1974) Discrete Numerical Methods in Physics and Engineering, Academic Press, New York.MATHGoogle Scholar
  10. Hunt, B.R. (1973) The application of constrained least-squares estimation to image restoration by digital computer, IEEE Trans. Comput. vol. C-22, 9: 805–812.CrossRefGoogle Scholar
  11. Incertis, F.C. (1981) On a novel matrix approach for linear space invariant 2-D deconvolutions, (in press) IEEE Trans. Automat. Contr. vol. AC-27, 4.Google Scholar
  12. Lancaster, P. (1970) Explicit solutions of linear matrix equations, SIAM J. Appl. Math., 12, 4: 554–556.Google Scholar
  13. Neudecker, H. (1969) A note on Kronecker matrix product and matrix equation systems, SIAM J. Appl. Math. 17: 603–606.Google Scholar
  14. Rabiner, L.R. and C.M. Rader (1972) Digital Signal Processing, IEEE Press, New York.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • F. C. Incertis
    • 1
  1. 1.IBM Madrid Scientific CenterUSA

Personalised recommendations