Image reconstruction from a complete set of geometric and complex moments

Barmak Honarvar, Raveendran Paramesran, Chern Loon Lim

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33 Citations (Scopus)


An image can be reconstructed from the finite set of its orthogonal moments. Since geometric and complex moment kernels do not satisfy orthogonality criterion, direct image reconstruction using them is deemed to be difficult. In this paper, we propose a technique to reconstruct an image from either geometric moments (GMs) or complex moments (CMs). We utilize a relationship between GMs and Stirling numbers of the second kind. Then, by using the invertibility property of the Stirling transform, the original image can be reconstructed from its complete set of either geometric or complex moments. Further, based on previous works on blur effects on a moment domain and using the proposed reconstruction methods, a formulation is shown to obtain an estimated original image from the degraded image moments and the blur parameter. The reconstruction performance of the proposed methods on blur images is presented to validate the theoretical framework.

Original languageEnglish
Pages (from-to)224-232
Number of pages9
JournalSignal Processing
Publication statusPublished - May 2014
Externally publishedYes


  • Complex moments
  • Gaussian blur
  • Geometric moments
  • Image reconstruction
  • Stirling transform

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