Random sensor arrays are examined from a compressive-sensing (CS) perspective. It is demonstrated that the natural random-array projections manifested by the media Green's function are consistent with the projection-type measurements associated with compressive sensing. This linkage allows the use of existing compressive-sensing theory to quantify the performance of random arrays, of interest for array design. The analysis demonstrates that the compressive-sensing theory is applicable to arrays in vacuum as well as in the presence of surrounding media; further, the presence of surrounding media with known properties may be used to improve array performance. © 2006 IEEE.