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A Geometry Driven Reconstruction Algorithm for the Mojette Transform

  • Nicolas Normand
  • Andrew Kingston
  • Pierre Évenou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4245)

Abstract

The Mojette transform is an entirely discrete form of the Radon transform developed in 1995. It is exactly invertible with both the forward and inverse transforms requiring only the addition operation. Over the last 10 years it has found many applications including image watermarking and encryption, tomographic reconstruction, robust data transmission and distributed data storage. This paper presents an elegant and efficient algorithm to directly apply the inverse Mojette transform. The method is derived from the inter-dependance of the “rational” projection vectors (p i ,q i ) which define the direction of projection over the parallel set of lines b = p i lq i k. Projection values are acquired by summing the value of image pixels, f(k,l), centered on these lines. The new inversion is up to 5 times faster than previously proposed methods and solves the redundancy issues of these methods.

Keywords

Conjugate Gradient Method Image Watermark Dependancy Graph Inversion Algorithm Projection Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nicolas Normand
    • 1
  • Andrew Kingston
    • 1
  • Pierre Évenou
    • 1
  1. 1.IRCCyN-IVCÉcole polytechnique de l’Université de NantesNantesFrance

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