Tuesday, May 07, 2013

How to find real-world applications for compressive sensing

Leslie Smith sent me the following today:
Dear Igor, 
I am especially glad that your talk "Compressive Sensing, what is it good for?" at Supelec (see http://nuit-blanche.blogspot.com/2013/04/compressive-sensing-what-is-it-good-for_24.html and http://nuit-blanche.blogspot.com/2013/04/sunday-monring-insight-compressive.html) went well because I gave a talk in a similar vein at the SPIE DSS 2013 conference on compressive sensing last Friday, May 3rd. The message I hoped to get across was that 'all of the excitement surrounding CS is necessary and appropriate for encouraging our creativity but we all must also take off our "rose colored glasses" and critically judge our ideas, methods and results relative to conventional imaging approaches.' Frankly, I was worried how my message would be received but the reception was surprisingly positive.
Hence I decided to make my paper "How to find real-world applications for compressive sensing" more widely available by posting it to ArXiv.org at http://arxiv.org/abs/1305.1199. This paper and the presentation are a result of some recent efforts to compare CS to conventional imaging methods for certain applications of interest to the Navy and contains a few 'lessons learned' from this experience. Please take a look at the abstract so you can decide if you want to mention this on your blog. 
Once again, thank you for your efforts with Nuit Blanche and related groups. I ended my presentation last Friday by highly recommending that anyone interested in CS should read your blog everyday. If every field of research had such a resource, this would revolutionize how science is done.
Best regards,
Thanks Leslie ! I like the fact that Leslie who is focused on an actual situation involving hardware and a full size experiment, uses one of the recent mostly mathematical inclined papers by Ben Adcok and Anders Hansen [1] as a way of expressing doubt for not implementing a straightforward vanilla compressive imaging approach (see also [1]).  I have several points to add to this inisght provided by Leslie but first, you first to read that paper: How to find real-world applications for compressive sensing by Leslie Smith. The abstract reads:
The potential of compressive sensing (CS) has spurred great interest in the research community and is a fast growing area of research. However, research translating CS theory into practical hardware and demonstrating clear and significant benefits with this hardware over current, conventional imaging techniques has been limited. This article helps researchers to find those niche applications where the CS approach provides substantial gain over conventional approaches by articulating lessons learned in finding one such application; sea skimming missile detection. As a proof of concept, it is demonstrated that a simplified CS missile detection architecture and algorithm provides comparable results to the conventional imaging approach but using a smaller FPA. The primary message is that all of the excitement surrounding CS is necessary and appropriate for encouraging our creativity but we all must also take off our "rose colored glasses" and critically judge our ideas, methods and results relative to conventional imaging approaches.

My first point is about compressive imager. As Mark Neifeld pointed out a while back [2], current cameras are already compressive:

Hence, the emphasis for compressive sensing application should often revolve around the detection of features of interest and see if further reduction of measurements can be accomplished easily.

My second point is on large phase space exploration. As I mentioned at the Supelec Q&A after the talk, what Compressive Sensing brought to light was that islands of knowledge [3], i.e fields where techniques are empirically but not mathematically grounded, need not be seen as defective. Rather the hard part in these "isolated" fields is figuring out what works and what doesn't. It's hard because the phase space is large and can quickly drown even the experts. What the mathematical grounding generally does is provide a framework for extensively exploring the phase space of what ought to work and what ought not. For instance, back in 1992, Donoho et al showed in Maximum Entropy and the Nearly Black Object that L1 was better than maximum entropy or least squares empirically on spectra. You can clearly note here two obvious issues:
  • while L1 does well on black objects in that paper, it probably could not do well on black objects + background featured in spectra shown in [5]. Only in 2004, with the mathematics of Candes, Romberg, Tao and Donoho, did we begin to understand why and how L1 could be applied to a spectrum like in [5] (psst... you need synthesis dictionaries and some admissibility conditions)
  • there is, to this date, no theory providing admissible measurement ensembles for maximum entropy solvers. As soon as there is one, watch out how fashionable these words "maximum entropy" will become....again
All this to say that while many folks may see the field just as a fashion fad or with pink colored glasses, the most important take away is the realization that we now have a deeper understanding on how we can sense the world around us. 

My last point is about the birth and death of certain technologies on the Technology Readiness Ladder. In order to be competitive you need to surf on the streamrollers not in front of them: choose wisely. This is probably a whole blog entry in and of itself.

Again, thanks Leslie for these discussions (some of which occurred on the Linkedin compressive sensing group )

[1] A Q&A with Ben Adcock and Anders Hansen: Infinite Dimensional Compressive Sensing, Generalized Sampling, Wavelet Crimes, Safe Zones and the Incoherence Barrier.
[2] Mark Neifeld's presentation made at the Duke-AFRL Meeting on Adaptation for Task-Specific Compressive Imaging
[3] Sunday Morning Insight: Game of Thrones and the History of Compressive Sensing
[4] Maximum Entropy and the Nearly Black Object by Donoho, Johnstone, Hoch and Stern
[5] Sunday Morning Insight: How to spot a compressive sensing system, the case of Fourier Transform Infra-Red Spectroscopy

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