  In this paper, we present a convolution neural network based method to
recover the light intensity distribution from the overlapped dispersive spectra
instead of adding an extra light path to capture it directly for the first
time. Then, we construct a single-path sub-Hadamard snapshot spectrometer based
on our previous dual-path snapshot spectrometer. In the proposed single-path
spectrometer, we use the reconstructed light intensity as the original light
intensity and recover high signal-to-noise ratio spectra successfully. Compared
with dual-path snapshot spectrometer, the network based single-path
spectrometer has a more compact structure and maintains snapshot and high
sensitivity. Abundant simulated and experimental results have demonstrated that
the proposed method can obtain a better reconstructed signal-to-noise ratio
spectrum than the dual-path sub-Hadamard spectrometer because of its higher
light throughput.
