The idea is to use the ability to describe single clouds through different means (ground laser, balloons...) so that one can infer the way light from the sun is being scattered inside the cloud. This information pretty much defines a multiplexing operation of the light coming from different parts of the Sun. This random multiplexing can then be deconvoluted using techniques used in Compressive Sensing to get an image of the Sun. The technical difficulty is finding the connection between the knowledge of the cloud obtained from other means and the resolution of the reconstructed image of the Sun. A good mitigating factor is the slow speed of clouds and their relative frozen state.
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