  The recent theory of compressive sensing leverages upon the structure of
signals to acquire them with much fewer measurements than was previously
thought necessary, and certainly well below the traditional Nyquist-Shannon
sampling rate. However, most implementations developed to take advantage of
this framework revolve around controlling the measurements with carefully
engineered material or acquisition sequences. Instead, we use the natural
randomness of wave propagation through multiply scattering media as an optimal
and instantaneous compressive imaging mechanism. Waves reflected from an object
are detected after propagation through a well-characterized complex medium.
Each local measurement thus contains global information about the object,
yielding a purely analog compressive sensing method. We experimentally
demonstrate the effectiveness of the proposed approach for optical imaging by
using a 300-micrometer thick layer of white paint as the compressive imaging
device. Scattering media are thus promising candidates for designing efficient
and compact compressive imagers.
