A Naturalness Preserving Transform

  • R. K. Rao Yarlagadda
  • John E. Hershey
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 383)


The use of (284) has been suggested as the basis for a “naturalness preserving” transform. (J. Hershey and R. Yarlagadda, 1983; R. Yarlagadda and J. Hershey, 1985.) Consider that we have an image encoded as a square matrix, P n, that consists of N x N pixels where N = 2 n . We form
$$ {\Pi_n} = ({\pi_{{ij}}}) = {\Psi_n}(\alpha ){P_n}{\Psi_n}(\alpha ) $$
If α is close to unity, then we will still be able to recognize the original image P n in Π n . By using (285d) we can recover P
$$ {P_n} = {\Psi_n}(\frac{\alpha }{{2\alpha - 1}}){\Pi_n}{\Psi_n}(\frac{\alpha }{{2\alpha - 1}}),\alpha \ne \frac{1}{2} $$
We can gain some further insight into Π n by exploring the Euclidean norm of (287). First we note that H
$$ {{\rm H}^{'}}_n = {C^{{\rm T}}}(\begin{array}{*{20}{c}} {{I_2}n - 1} 0 \\ 0 { - {I_2}n - 1} \\ \end{array} )C $$
where C is an orthogonal matrix of order 2 n and I 2 n-1 is an identity matrix of order 2 n-1.


Original Image Orthogonal Matrix Inverse Transforming Iterative Technique Spectral Norm 
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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • R. K. Rao Yarlagadda
    • 1
  • John E. Hershey
    • 2
  1. 1.Oklahoma State UniversityUSA
  2. 2.General Electric Corporate Research & Development CenterUSA

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