  In the Cognitive Compressive Sensing (CCS) problem, a Cognitive Receiver (CR)
seeks to optimize the reward obtained by sensing an underlying $N$ dimensional
random vector, by collecting at most $K$ arbitrary projections of it. The $N$
components of the latent vector represent sub-channels states, that change
dynamically from "busy" to "idle" and vice versa, as a Markov chain that is
biased towards producing sparse vectors. To identify the optimal strategy we
formulate the Multi-Armed Bandit Compressive Sensing (MAB-CS) problem,
generalizing the popular Cognitive Spectrum Sensing model, in which the CR can
sense $K$ out of the $N$ sub-channels, as well as the typical static setting of
Compressive Sensing, in which the CR observes $K$ linear combinations of the
$N$ dimensional sparse vector. The CR opportunistic choice of the sensing
matrix should balance the desire of revealing the state of as many dimensions
of the latent vector as possible, while not exceeding the limits beyond which
the vector support is no longer uniquely identifiable.
