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Random Matrix Theory for Modeling the Eigenvalue Distribution of Images Under Upscaling

  • David Vázquez-PadínEmail author
  • Fernando Pérez-González
  • Pedro Comesaña-Alfaro
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 766)

Abstract

The stochastic representation of digital images through a two-dimensional autoregressive (2D-AR) model offers a proper way to approximate the empirical distribution of the eigenvalues coming from genuine images. By considering this model, we apply random matrix theory to analytically derive the asymptotic eigenvalue distribution of causal 2D-AR random fields that have undergone an upscaling operation with a particular interpolation kernel. This eigenvalue characterization is useful in developing new forensic techniques for image resampling detection since we can use theoretical bounds to drive the decision of detectors based on subspace decomposition. Moreover, experimental results with real images show that the obtained asymptotic limits turn out to be excellent approximations, even when working with images of small size.

Keywords

Image forensics Marčenko-Pastur law Random matrix theory Resampling detection Two-dimensional autoregressive model 

Notes

Acknowledgments

This work is funded by the Agencia Estatal de Investigación (Spain) and the European Regional Development Fund (ERDF) under project WINTER (TEC2016-76409-C2-2-R), and by the Xunta de Galicia and the ERDF under projects Agrupación Estratéxica Consolidada de Galicia accreditation 2016–2019 and Red Temática RedTEIC 2017–2018.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • David Vázquez-Padín
    • 1
    Email author
  • Fernando Pérez-González
    • 1
  • Pedro Comesaña-Alfaro
    • 1
  1. 1.Signal Theory and Communications DepartmentUniversity of VigoVigoSpain

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