Scale invariant images in astronomy through the lens of multifractal modeling

Pierre Chainais (1, 2, 3) , Véronique Delouille (4) , Jean-François Hochedez (5)

1 Centrale Lille
2 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
3 LAGIS-SI
4 Solar Physics Department [Brussels]
5 HELIOS - LATMOS

The mystery of the dynamics of the Sun is even deeper when it is quiet, i.e. when there are no coherent areas structured by strong magnetic field and called active regions. The solar corona is observed by extreme UV spatial telescopes for which higher resolutions are always desired: the best pixel resolution currently achievable is 500 km which still leaves room for crucial hidden details. We present our work on the analysis of quiet Sun images of the corona. These images exhibit multifractal properties and a model based on scale invariant stochastic processes, called fractionally integrated compound Poisson cascades, reproduces their main statistical properties. We show that it can be used to develop a virtual super-resolution method that proposes plausible predictions of the high resolution information hidden below the pixel size of present observations. Such images may help physicists to test and calibrate on-board processing algorithms for future missions.

Mots clés: self-similarity; multifractal analysis; stochastic processes; extrapolation; solar corona

Domaines: Traitement des images [eess.IV]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Astrophysique stellaire et solaire [astro-ph.SR]; Astrophysique stellaire et solaire [astro-ph.SR]; Physique Atmosphérique et Océanique [physics.ao-ph]

Pierre Chainais, Véronique Delouille, Jean-François Hochedez. Scale invariant images in astronomy through the lens of multifractal modeling. 18th IEEE International Conference on Image Processing (ICIP2011),, Sep 2011, Brussels, Belgium. pp.1309 -1312, ⟨10.1109/ICIP.2011.6115676⟩. ⟨hal-00657779⟩