Nonconvex low-rank regularization method for video snapshot compressive imaging

The reconstruction of snapshot compressive imaging (SCI) presents a significant challenge in signal processing. The primary goal of SCI is to employ a low-dimensional sensor to capture high-dimensional data in a compressed form. As a result, compared to traditional compressive sensing, SCI emphasizes capturing structural information and enhancing the reconstruction quality of high-dimensional videos and hyperspectral images. This paper proposes a novel SCI reconstruction method by integrating non-convex regularization approximation in conjunction with rank minimization. Furthermore, we address the characterization of structural information by leveraging nonlocal self-similarity across video frames to improve the reconstruction quality. We also develop an optimization algorithm based on the alternating direction method of multipliers (ADMM) to solve the model and provide a convergence algorithm analysis. Extensive experiments demonstrate that the proposed approach can potentially reconstruct SCI effectively.