Theoretical Analysis of Binary Masks in Snapshot Compressive Imaging Systems

TL;DR

This paper provides a comprehensive theoretical analysis of binary masks in snapshot compressive imaging systems, revealing optimal mask probabilities and extending understanding to Markov-generated masks, which aids in system design.

Contribution

It offers the first detailed theoretical characterization of binary masks in SCI, including optimal mask probabilities and performance analysis for Markov-dependent masks.

Findings

Optimal non-zero element probability is less than 0.5.

Binary iid masks with this probability improve system performance.

Markov-dependent masks have distinct performance characteristics.

Abstract

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.