Theoretical Characterization of Effect of Masks in Snapshot Compressive Imaging

.Snapshot compressive imaging (SCI) refers to the recovery of three-dimensional data cubes, such as videos or hyperspectral images, from their two-dimensional projections, which are generated by a special encoding of the data with a mask. SCI systems commonly use binary-valued masks that follow certain physical constraints. Optimizing these masks subject to these constraints is expected to improve system performance. While prior theoretical analysis of SCI systems has primarily focused on independent and identically distributed Gaussian masks, recent empirical, data-driven mask optimizations yield structured and sometimes interpretable patterns. However, such empirical optimizations typically involve computationally intensive joint procedures that are expected to be suboptimal due to the nonconvexity and complexity of the optimization. In this paper, we analytically characterize the performance of SCI systems employing binary masks and leverage our analysis to optimize hardware parameters. Our findings provide a comprehensive and fundamental understanding of the role of binary masks, with both independent and dependent elements, and their optimization. We also present simulation results that confirm our theoretical findings and further illuminate different aspects of mask design.