  Snapshot compressive imaging (SCI) systems have gained significant attention
in recent years. While previous theoretical studies have primarily focused on
the performance analysis of Gaussian masks, practical SCI systems often employ
binary-valued masks. Furthermore, recent research has demonstrated that
optimized binary masks can significantly enhance system performance. In this
paper, we present a comprehensive theoretical characterization of binary masks
and their impact on SCI system performance. Initially, we investigate the
scenario where the masks are binary and independently identically distributed
(iid), revealing a noteworthy finding that aligns with prior numerical results.
Specifically, we show that the optimal probability of non-zero elements in the
masks is smaller than 0.5. This result provides valuable insights into the
design and optimization of binary masks for SCI systems, facilitating further
advancements in the field. Additionally, we extend our analysis to characterize
the performance of SCI systems where the mask entries are not independent but
are generated based on a stationary first-order Markov process. Overall, our
theoretical framework offers a comprehensive understanding of the performance
implications associated with binary masks in SCI systems.
