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.
Bibliographical noteFunding Information:
This work was supported by the European Research Council (Grant Nu278025), the Emergence(s) program from the City of Paris, and LABEX WIFI (Laboratory of Excellence within the French Program ‘‘Investments for the Future’’) under references ANR-10-LABX-24 and ANR-10-IDEX-0001-02 PSL*. G.C. is supported by the Austrian Science Fund (FWF) START-project FLAME (Y 551-N13). O.K. is supported by the Marie Curie intra-European fellowship for career development (IEF) and the Rothschild fellowship. I.C. would like to thank the Physics arXiv Blog for drawing his attention to opaque lenses and Ms. Iris Carron for her typesetting support.