I'm an undergrad in a lab that focuses on compressed sensing (and we're getting more into sparse machine learning). Sparsity is a way of saying that most of th

I'm an undergrad in a lab that focuses on compressed sensing (and we're getting more into sparse machine learning). Sparsity is a way of saying that most of the data you collect is related in some way. One advantage of sparsity (and there are many more) is sampling at sub-Nyquist rates[0] and still being able reconstruct the signal precisely. Why? Because the signal is sparse in the Fourier domain -- there are only a few frequencies present in the signal. Reading this article, I had some issues with this quote: > According to Candes, you could take half the samples (16) and rerun the test. If it is positive, the infected person is in this group; if negative, the culprit is in the other half. You can continue to whittle down the possibilities by once again dividing the group in half and running the test again. That's just a simple binary search[1]. Instead, why not collect other information? Collect some genetic information, lifestyle habits, living location, etc. Then I believe (that's a strong I believe) you could optimize even further by testing patients that have some of these traits in common -- you'd have groups of unequal sizes based on who you think has the disease. This corresponds to sparsity. Most traits don't matter but a select few do. To see real-world results of sparsity, we're able to reconstruct precise approximations after we assume our input is sparse in the wavelet basis (corresponding to many areas of the same color). We're able to push this sampling rate down to ~6% for simple images by doing a "sample, compute" method. The reconstructed approximation and sampled locations are shown in this image[2] [0]:https://en.wikipedia.org/wiki/Binary_search https://en.wikipedia.org/wiki/Binary_search [1]:https://en.wikipedia.org/wiki/Nyquist_rate https://en.wikipedia.org/wiki/Nyquist_rate [2]:http://imgur.com/PmYpze6 http://imgur.com/PmYpze6