Group Testing and Compressive Sensing

As Bernard Beauzamy will present a paper at the Aerospace Testing, Design and Manufacturing 2009 Seminar in Munich, I was reminded that he refers to a testing procedure called "group testing" as a solution for companies to comply with the E.U. REACH regulations without incurring major financial losses.

There is a clear connection between group testing and compressive sensing, a subject area for which I perform some type of Technology Watch on a blog: http://nuit-blanche.blogspot.com . More information can be found in either the repository at Rice University or in the Compressive Sensing Big Picture page.

Initially, Group testing was used extensively by the U.S. Army in the 1940's in order to screen for syphilis in their troops. The procedure enabled enormous savings since the detection kits were pricey at the time. One can read the first few paragraphs of this report by Joel Tropp and Anna Gilbert on the connection between compressive sensing and group testing in Signal Recovery From Random Measurements via Orthogonal Matching Pursuit: The Gaussian Case. Also of interest is the video by Anna Gilbert who presented their latest results using this technique (CS + group testing) on bio chips called SNPs (in this experiment they do not use Gaussian matrices but rather sparser constructs called Expander Graphs). I pointed to it before and the video is here. While current results are OK for the time being, it may be difficult for this type of solution to convert the folks in pure bio research unless there is a tremendous savings for the detection of a certain disease. On the other hand, if there is an important financial gain and this testing procedure is Ok'ed by the proper regulation authorities, there is a likely chance that commercial companies could adopt this type of technique faster.