Optimized Coded Apertures for Hyperspectral Image Reconstruction via Variant RIP Constant

When modulating hyperspectral scenes by the coded aperture snapshot spectral imagery (CASSI) system, binary coded apertures are used to ease data acquisition, storage and transmission. In CASSI, the reconstruction performance relies on the correlation of coded apertures entries. Since the traditional coded apertures lead to suboptimal reconstruction solutions, the modified methods have been investigated to enhance reconstruction performance. However, none of them exploit the underlying sensing matrix structures, which determine the coded aperture entries in turn. In this letter, a novel coded aperture optimization approach for CASSI is proposed. Firstly, the coded aperture optimization is regarded as a sensing process. Secondly, a variant constant is defined as the function of coded aperture entries, based on the restricted isometry property conditions for sensing matrix. Both the optimal constant and its sensing matrix are achieved by Alternating direction method of multipliers. Finally, the optimized coded apertures are attained via a linear matrix considering the structure-preserving characteristics of sensing matrix. Simulations demonstrate the effectiveness and superiority of the proposed coded apertures.