Hyperspectral images (HSIs) can provide rich spatial and spectral information with extensive application prospects. Recently, several methods using convolutional neural networks (CNNs) to reconstruct HSIs have been developed. However, most deep learning methods fit a brute-force mapping relationship between the compressive and standard HSIs. Thus, the learned mapping would be invalid when the observation data deviate from the training data. To recover the three-dimensional HSIs from two-dimensional compressive images, we present dual-camera equipment with a physics-informed self-supervising CNN method based on a coded aperture snapshot spectral imaging system. Our method effectively exploits the spatial-spectral relativization from the coded spectral information and forms a self-supervising system based on the camera quantum effect model. The experimental results show that our method can be adapted to a wide imaging environment with good performance. In addition, compared with most of the network-based methods, our system does not require a dedicated dataset for pre-training. Therefore, it has greater scenario adaptability and better generalization ability. Meanwhile, our system can be constantly fine-tuned and self-improved in real-life scenarios.