Security analysis of rakeness-based compressed sensing

Compressed sensing, further to its ability of reducing resources spent in signal acquisition, may be seen as an implicit private-key encryption scheme. The level of achievable secrecy has been analyzed in the most classical settings, when the sensing matrix is made of independent and identically distributed entries. Yet, it is known that substantially improved acquisition can be achieved by tuning the statistics of such a matrix. The effect of such an optimization on the robustness with respect to classical cryptographic attacks is analyzed here.