In the comment section of the previous entry, Laurent Jacques highlighted the fact that if one were to use clouds as a mechanism for performing imaging, one would need to figure out the cloud Point Spread Function (PSF). He is totally right. As in the Random Lens Imager case, the calibration step is essential to determine the point spread function (PSF). Hence the cloud PSF calibration needs to happen very fast indeed. Compressive Sensing gives a way of reducing the number of trials needed to determine the full PSF as can be seen in .
In a Lidar mode, each measurement goes at the speed of light and so even if one has to perform many of them, the calibration is expected to go faster than most turbulence of interest in the cloud. Now the problem is to scan the whole cloud fast enough. Can the reduction of samples afforded by compressive sensing enable a rapid scanning, this is the question to answer.
While we are on the subject of using Nature as an imaging tool,
Luc Arnold for instance uses the Moon as a mirror to find out vegetation on Earth . Since we know the Moon's surface with a certain accuracy, how can we use this information to obtain a better Moon PSF and eventually better images of Earth ? Let us note that this type of investigation (imaging Earth with the Moon with accuracy) is not interesting to the astronomy folks as the Moon-Earth imaging example is an example for detecting chemical elements on exoplanets. Therefore, they do not care about the details of the Moon's surface since they will not know it in real observations.