Fast spectrum reconstruction based-on interpretable network with physical model involved

Computational spectrometers has a great potential for real-time detection in site measurements. Reconstruction algorithms play a pivotal role. Traditional reconstruction algorithms, while demanding low computational resources and enabling real-time measurements, often face challenges in achieving high reconstruction accuracy. Deep learning-based methods offer high-precision reconstruction but require more computational resources and lack interpretability. In this work, we propose an end-to-end interpretable unfolding network that translates the iterative process of the ADMM algorithm into a network layer and autonomously learns sparse basis matrices, ensuring that each network parameter has a clear physical meaning. The performance of this algorithm was validated on two synthetic spectrum datasets and a measured spectrum dataset. The results demonstrate that our method not only ensures high reconstruction accuracy and robustness but also reduces the computational resources. Collectively, this algorithm avoids the black-box characteristics of neural networks and is with physical model involved, which has significant potential to enable high-precision real-time measurements in computational spectroscopy.