Deconvolution of Gaussian and Other Kernels

  • Johan Philip
Part of the Progress in Scientific Computing book series (PSC, volume 2)


We consider the numerical solution of the convolution equation h * f = d for various nonnegative kernels h. Obviously, the Dirac measure is the easiest kernel to deconvolve. In a certain sense, there also exists a unique most difficult kernel to deconvolve, namely the Gaussian exp(−x2). A method for deconvolution of the Gaussian is suggested.


Discrete Fourier Transformation Generalize Inverse Dirac Measure Convolution Equation Deconvolution Problem 
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  1. [1]
    Andrews, H.C., and Hunt, B.R., “Digital Image Restoration”, Prentice Hall Englewood Cliffs, 1977Google Scholar
  2. [2]
    Carasso, A.S., Sanderson, J.G. and Hyman, J.M., “Digital Removal of Random Media Image Degradations by Solving the Diffusion Equation Backwards in Time”, SIAM J. Numer. Anal, vol.15, no.2, April 1978Google Scholar
  3. [3]
    Cramer, H., “Mathematical Methods of Statistics” Princeton University Press 1946Google Scholar
  4. [4]
    Elden, L., “A Program for Interactive Regularization, Part I”, Report LiTH-Mat-R-79-25, Linköping University, SwedenGoogle Scholar
  5. [5]
    Nashed, M.Z. “Generalized Inverses and Applications”, Academic Press 1976Google Scholar
  6. [6]
    Philip, J., “Digital Image and Spectrum Restoration by Quadratic Programming and by Modified Fourier Transformation”, IEEE Trans. PAMI vol. 1, no.4, Oct. 1979Google Scholar
  7. [7]
    Philip, J., “Error Analysis of the Derivative and Correction Methods for Digital Image and Spectrum Restoration”, TRITA-MAT-1981-16, Mathematics, Royal Institute of Technology, Stockholm, SwedenGoogle Scholar
  8. [8]
    Philip, J., “Deconvolution of Gaussian Kernels”, TRITA-MAT-1982-4, Mathematics, Royal Institute of Technology, 10044-Stockholm, Sweden. (Submitted to SIAM J. Numerical Analysis)Google Scholar
  9. [9]
    Tikhonov, A.N., “Solution of Incorrectly Formulated Problems and the Regularization Method”, Dokl. Akad.Nauk, SSSR 151 (1963), pp.501–504 = Soviet Math. Dokl.4 (1963) pp. 1035-1038MathSciNetGoogle Scholar

Copyright information

© Birkhäuser Boston 1983

Authors and Affiliations

  • Johan Philip

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