Note on the noise reduction in spectroscopic detection with compressed sensing

Spectroscopy sampling along delay time is typically performed with uniform delay spacing, which has to be low enough to satisfy the Nyquist-Shannon sampling theorem. The sampling theorem puts the lower bound for the sampling rate to ensure accurate resolution of the spectral features. However, this bound can be relaxed by leveraging prior knowledge of the signals, such as sparsity. Compressed sensing, a under-sampling technique successfully applied to spatial measurements (e.g., single-pixel imaging), has yet to be fully explored for the spectral measurements especially for the temporal sampling. In this work, we investigate the capability of compressed sensing for improving the temporal spectroscopic measurements to mitigate both measurement noise and intrinsic noise. By applying compressed sensing to single-shot pump-probe data, we demonstrate its effectiveness in noise reduction. Additionally, we propose a feasible experimental scheme using a digital mirror device to implement compressed sensing for temporal sampling. This approach provides a promising method for spectroscopy to reduce the signal noise and the number of sample measurements.