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.