CS: Deciphering subsampled data: adaptive compressive sampling as a principle of brain communication

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Today's paper is about an important problem (* see below for a definition of an important problem) . Not only it is not about reconstruction, it's not even about the measurement matrix as it is supposed to be unknown. I cannot wait to see how phase transition in the context of ACS (the following paper) could be a good model for the understanding of neurological diseases, but more importantly how this model could be used as a quantitative tool for correlation with other observed data (such as fMRI,...) Without further due here it is: Deciphering subsampled data: adaptive compressive sampling as a principle of brain communication by Guy Isely, Christopher J. Hillar, Friedrich T. Sommer. The abstract reads:

A new algorithm is proposed for a) unsupervised learning of sparse representations from subsampled measurements and b) estimating the parameters required for linearly reconstructing signals from the sparse codes. We verify that the new algorithm performs efficient data compression on par with the recent method of compressive sampling. Further, we demonstrate that the algorithm performs robustly when stacked in several stages or when applied in undercomplete or overcomplete situations. The new algorithm can explain how neural populations in the brain that receive subsampled input through fiber bottlenecks are able to form coherent response properties.

* I take the definition of an important problem from a talk by Richard Hamming which you may have seen at the end of my page:

....Let me warn you, `important problem' must be phrased carefully. The three outstanding problems in physics, in a certain sense, were never worked on while I was at Bell Labs. By important I mean guaranteed a Nobel Prize and any sum of money you want to mention. We didn't work on (1) time travel, (2) teleportation, and (3) antigravity. They are not important problems because we do not have an attack. It's not the consequence that makes a problem important, it is that you have a reasonable attack. That is what makes a problem important. When I say that most scientists don't work on important problems, I mean it in that sense. The average scientist, so far as I can make out, spends almost all his time working on problems which he believes will not be important and he also doesn't believe that they will lead to important problems.

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