Hyperspectral Image Reconstruction of SD-CASSI Based on Nonlocal Low-Rank Tensor Prior

In single disperser coded aperture snapshot spectral imaging (SD-CASSI) systems, many methods have been developed to reconstruct hyperspectral images (HSIs) from compressed measurements. Among these, deep learning (DL)-based methods have stood out, relying on powerful DL networks. However, the solidified structure of DL-based methods limits their adaptability. Moreover, they are often based on a model that neglects the dispersion process and instead emphasizes the encoding-compression process. Furthermore, research on optimization-based methods designed especially for SD-CASSI is lacking. In this article, we propose a comprehensive two-step projection imaging model for SD-CASSI that includes both spectral shearing projection and encoding-compression projection. Based on this model, we derive a tensor-based optimization framework that incorporates with the nonlocal low-rank tensor (NLRT) prior. In particular, NLRT extracts inherent spatial structural information from the measurements and employs it to guide the clustering of spatial-spectral similar HSI blocks. A CANDECOMP/PARAFAC (CP) low-rank regularizer is introduced to constrain the low-rank property of HSI block clusters. After that, we develop a solution framework based on the alternating direction method of multiplier (ADMM) approach. Comprehensive experiments demonstrate that our NLRT method outperforms state-of-the-art methods in terms of flexibility and performance. The source code and data of this article are publicly available at https://github.com/sdnjyxr/NLRT.