Journal of Mathematical Imaging and Vision

, Volume 39, Issue 1, pp 28–44 | Cite as

Virtual Super Resolution of Scale Invariant Textured Images Using Multifractal Stochastic Processes

  • Pierre ChainaisEmail author
  • Émilie Kœnig
  • Véronique Delouille
  • Jean-François Hochedez


We present a new method of magnification for textured images featuring scale invariance properties. This work is originally motivated by an application to astronomical images. One goal is to propose a method to quantitatively predict statistical and visual properties of images taken by a forthcoming higher resolution telescope from older images at lower resolution. This is done by performing a virtual super resolution using a family of scale invariant stochastic processes, namely compound Poisson cascades, and fractional integration. The procedure preserves the visual aspect as well as the statistical properties of the initial image. An augmentation of information is performed by locally adding random small scale details below the initial pixel size. This extrapolation procedure yields a potentially infinite number of magnified versions of an image. It allows for large magnification factors (virtually infinite) and is physically conservative: zooming out to the initial resolution yields the initial image back. The (virtually) super resolved images can be used to predict the quality of future observations as well as to develop and test compression or denoising techniques.


Natural images Scale invariance Multifractal analysis Extrapolation Enhancement Infinitely divisible cascades 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Pierre Chainais
    • 1
    Email author
  • Émilie Kœnig
    • 1
  • Véronique Delouille
    • 2
  • Jean-François Hochedez
    • 2
  1. 1.Université Blaise Pascal CNRS UMR 6158, LIMOSClermont UniversitéClermont-FerrandFrance
  2. 2.Royal Observatory of BelgiumBrusselsBelgium

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