Compressive Earth Observatory: An Insight from AIRS/AMSU Retrievals (and a comment)

This is exciting but I have included my thoughts below:

Compressive Earth Observatory: An Insight from AIRS/AMSU Retrievals by Ardeshir Mohammad Ebtehaj, Efi Foufoula-Georgiou, Gilad Lerman, Rafael Luis Bras

We demonstrate that the global fields of temperature, humidity and geopotential heights admit a nearly sparse representation in the wavelet domain, offering a viable path forward to explore new paradigms of sparsity-promoting assimilation and compressive retrieval of spaceborne earth observations. We illustrate this idea using retrieval products of the Atmospheric Infrared Sounder (AIRS) and Advanced Microwave Sounding Unit (AMSU) on board the Aqua satellite. The results reveal that the sparsity of the fields of temperature and geopotential height is relatively pressure-independent while atmospheric humidity fields are typically less sparse at higher pressures. Using the sparsity prior, we provide evidence that the global variability of these land-atmospheric states can be accurately estimated from space in a compressed form, using a small set of randomly chosen measurements/retrievals.

 
From the paper we can see:

In other words, our sensing matrices are obtained from an identity matrix in which we have randomly eliminated 55% and 65% of its rows, respectively. In this case, it is easy to show that the sensing matrix has the RIP property for which the CS in (5) can lead to an accurate and successful recovery (see, Section B in Appendix). 

 

so it looks like inpainting and from the conclusion, we have:

 

 

 While progress has been made recently in developing sparse digital image acquisition in visible bands [33], development of sparse-remote-sensing instruments for earth observations from space in microwave and infrared wavelengths remains an important challenge in the coming years. However, our results suggest that, even under the current sensing protocols, transmitting, storing, and processing only a few randomly chosen pixel-samples of the primary land-atmospheric states can be advantageously exploited for a speedy reconstruction of the entire sensor’s field of view with a notable degree of accuracy. The implications of such a capability cannot be overstated for real-time tracking and data assimilation of extreme land-atmospheric phenomena in global early warning systems.

 I like the fact that the findings put the current remote sensing systems within the larger view on how to do sampling and how future instruments might be an extension of that through the use of compressive sensing. 

 

There is the potential for impressionable kids to think that compressive sensing and inpainting might generally be the same as the title of this article on Wired might imply. It is a dichotomy that is difficult to communicate and to this day, we still have people mixing up compressive sensing and inpainting. The idea is very difficult to eradicate that in order to perform compressive sensing, you generally oversample the signal so that measurements are actually redundant. Inpainting on the other hand makes it look like we are getting something for nothing (by avoiding sampling in some part of the signal - an image in general - we can recover the full image), i.e. the algorithm somehow discovers something that was never sensed in the first place. This is not what we have here.

These two views can be coincident or blurred only if you show that the field being measured is actually spread or incoherent with the measurement system being used (here it is point like). This is why the authors of the paper spend a large part of the paper showing that the field is part of a dictionary (low frequency wavelets) and that sampling at specific locations is an adequate incoherent measurement system....at that scale.

 

I wish the authors had written a sentence on that because there are a lot of impressionable kids on the interwebs.

 

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