In situ compressive sensing

Compressive sensing (CS) is a framework that exploits the compressible character of most natural signals, allowing the accurate measurement of an m-dimensional real signal u in terms of n << m real measurements v. The CS measurements may be represented in terms of an n x m matrix that defines the linear relationship between v and u. In this paper we demonstrate that similar linear mappings of the form u -> nu are manifested naturally by wave propagation in complex media, and therefore in situ CS measurements may be performed simply by exploiting the complex propagation and scattering properties of natural environments. A similar phenomenon is observed in time-reversal imaging, to which connections are made. In addition to presenting the basic in situ CS framework, a simple but practical example problem is considered.