Abstract: Computational spectral imaging has been striving to capture the spectral information of the dynamic world in the last few decades. In this paper, we propose an interpretable neural network for computational spectral imaging. First, we introduce a novel data-driven prior that can adaptively exploit both the local and non-local correlations among the spectral image. Our data-driven prior is integrated as a regularizer into the reconstruction problem. Then, we propose to unroll the reconstruction problem into an optimization-inspired deep neural network. The architecture of the network has high interpretability by explicitly characterizing the image correlation and the system imaging model. Finally, we learn the complete parameters in the network through end-to-end training, enabling robust performance with high spatial-spectral fidelity. Extensive simulation and hardware experiments validate the superior performance of our method over state-of-the-art methods.