The world largely consists of continuous signals.  For example, the electromagnetic field in a radio signal varies with time in a continuous fashion.  Likewise for audio signals and images.  When it comes time to store or process the signal on a computer, it is typical to retain only the signal at a set of discrete successive times separated by an interval that is sufficiently small so that none of the essential rapidly varying information is lost.  How to choose this interval is determined by the famous Nyquist-Shannon sampling theorem.  Some signals, however, may be very sparse.  That is, the signal might be zero most of the time, so sampling at a rate determined by the Nyquist-Shannon limit may result in the retention of lots of data that are just zeros.  (More generally, the signal might be sparse in some other domain.)  Thus, storage or transmission of sparse signals sampled in the conventional way can be extremely inefficient.

Compressive sensing was devised by Justin Romberg of ECE and others to sample a sparse signal below the Nyquist-Shannon limit, but nonetheless to permit its faithful reconstruction, and thus to store and transmit sparse signals in a very efficient fashion.  Compression is the process of sampling and storing the sparse signal, while sensing is the process of reconstructing the original signal.  Compression relies on having at hand large strings of random (or sufficiently random-looking) numbers to populate the compression matrix needed to compress the data. Such strings of pseudo-random numbers are typically generated on a digital computer.  Nevertheless, for the ultimate in high speed and simplicity, it is desirable to generate the string of random-like numbers, and ultimately carry out the compression itself, not only at speeds not readily attained on a conventional computer, but also physically.  In recent work published in Scientific Reports [reference here], together with collaborator Damien Rontani of Centrale-Supélec in Metz, France, Profs. David Citrin and Alexandre Locquet of ECE with PhD students Daeyoung Choi (ECE) and C.-Y. Chang (Physics) have used a chaotic optical signal produced by an external-cavity semiconductor laser to generate sufficiently random-like numbers at very high rate, based on the sub-100 picosecond timescale determining the dynamics of the laser.  The team demonstrated efficient compression followed by high-fidelity reconstruction of images using this technique.  The work at Georgia Tech was conducted at the GT-CNRS UMI 2958 laboratory (http://gtl-umi.gatech.edu) at Georgia Tech Lorraine (lorraine.gatech.edu) in Metz, France where the Nonlinear Dynamics and Optics group led by Profs. Citrin and Locquet.  According to Citrin, "This work is exciting as it opens the way to ultrahigh-speed compression of sparse signals--and we hope soon in a way to be carried out in the physical layer."

View "Compressive Sensing with Optical Chaos" in Scientific Reports at this link.