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.

翻译：快照压缩成像（SCI）系统近年来引起了广泛关注。尽管先前的理论研究主要关注高斯掩膜的性能分析，但实际SCI系统通常采用二元掩膜。此外，近期研究表明，优化后的二元掩膜能够显著提升系统性能。本文对二元掩膜及其对SCI系统性能的影响进行了全面的理论刻画。首先，我们研究了掩膜为独立同分布（iid）二元变量的场景，揭示了一个与先前数值结果一致的重要发现：掩膜非零元素的最优概率小于0.5。这一结果为SCI系统中二元掩膜的设计与优化提供了宝贵的见解，有助于推动该领域的进一步发展。此外，我们将分析扩展至掩膜元素非独立、而是基于平稳一阶马尔可夫过程生成的SCI系统性能刻画。总体而言，我们的理论框架为理解SCI系统中二元掩膜的性能影响提供了全面的视角。