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 signal u in terms of n ≪ m measurements v. The CS measurements may be represented in terms of an n × m matrix that defines the linear relationship between v and u. In this paper, we demonstrate that similar linear mappings of the form u → v are manifested naturally by wave propagation in general media, and therefore in situ CS measurements may be performed simply by exploiting the propagation and scattering properties of natural environments. The connection between the propagation medium and the basis in which u is sparsely rendered is quantified in terms of a mutual-coherence factor, which plays an important role in defining the number of required in situ CS measurements. In addition to presenting the basic in situ CS framework, a simple but practical example problem is considered in detail from multiple perspectives. © 2008 IOP Publishing Ltd.