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 [2].
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 [1]. 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.
5 comments:
Imagine a Demon (a relative of Maxwell's demon?) with complete knowledge of the entire scene, cameras, mathematics, optics, and s tiny paint brush.
Could such a demon touch up the scene in a subpixel manner such that the normal imaging system sees the same image as before, while the random imager sees something wildly different? It seems to me that it could. The touched up scene would be highly improbable I suppose.
I find this fascinating, as much as I understand this.
I don't think it would but being random there would be little control about the capability for superresolution.
Cheers,
Igor.
Is this demon interesting? I don't want to waste your time!
It seems to me that such a demon could defeat superresolution. To the demon, nothing is random, he knows everything, past and future. His only power is his ability to paint very fine detail in such a way that the detail looks like one thing at one resolution and another completely differnt thing at another resolution.
Salvador Dali made paintings like this years ago.
I really want to understand this.
Thanks,
Michael
Michael,
Thanks for your comment, I am sure a lot a people are asking themselves similar questions, so this is a good exercise.
In effect, while the random medium is indeed random, the calibration step I am mentioning is really about having a full characterization of it. So, in effect, we are building the demon. Once we know everything about the random medium we can use the medium to image.
Compressed sensing tells you that if the scene of interest is sparse, the random medium (known after being characterized) and a certain number of measurement done through this medium allows one to know perfectly the scene of interest. Only the physics will put some constraints on what you can see.
Hope this answer your question, if not let me know.
Igor.
Thanks,
Thanks. Much food for thought.
Michael
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