A Comparison of Statistical Regularization and Fourier Extrapolation Methods for Numerical Deconvolution

  • A. R. Davies
  • M. Iqbal
  • K. Maleknejad
  • T. C. Redshaw
Part of the Progress in Scientific Computing book series (PSC, volume 2)


The Fredholm integral equation of the first kind of convolution type:
$${\rm{(Kf)}}({\rm{x}})\> \equiv \>\int_{ - \infty }^\infty {{\rm{k(x - y)}}} \;{\rm{f(y)dy}}\;{\rm{ = }}\;{\rm{g(x),}}\;{\rm{ - }}\infty {\rm{ < }}\;{\rm{y}}\;{\rm{ < }}\;\infty {\rm{,}}\>$$
occurs widely in the applied sciences. k and g are known kernel and data functions, respectively, and f is to be found. We shall assume that f, g and k lie in suitable function spaces, such as L2(R), so that their Fourier transforms (FTs) exist. (∧ will denote FTs, and ∨ inverse FTs).


Noise Level Statistical Regularization Fourier Coefficient Fredholm Integral Equation Deconvolution Problem 
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Copyright information

© Birkhäuser Boston 1983

Authors and Affiliations

  • A. R. Davies
  • M. Iqbal
  • K. Maleknejad
  • T. C. Redshaw

There are no affiliations available

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