Compressed sensing under strong noise. Application to imaging through multiply scattering media

Compressive sensing exploits the structure of signals to acquire them with fewer measurements than required by the Nyquist-Shannon theory. However, the design of practical compressive sensing hardware raises several issues. First, one has to elicit a measurement mechanism that exhibits adequate incoherence properties. Second, the system should be robust to noise, whether it be measurement noise, or calibration noise, i.e. discrepancies between theoretical and actual measurement matrices. Third, to improve performance in the case of strong noise, it is not clear whether one should increase the number of sensors, or rather take several measurements, thus settling in the multiple measurement vector scenario (MMV). Here, we first show how measurement matrices may be estimated by calibration instead of being assumed perfectly known, and second that if the noise level reaches a few percents of the signal level, MMV is the only way to sample sparse signals at sub-Nyquist sampling rates.