  Noise manifests ubiquitously in nonlinear spectroscopy, where multiple
sources contribute to experimental signals generating interrelated unwanted
components, from random point-wise fluctuations to structured baseline signals.
Mitigating strategies are usually heuristic, depending on subjective biases
like the setting of parameters in data analysis algorithms and the removal
order of the unwanted components. We propose a data-driven frequency-domain
denoiser based on a convolutional neural network with kernels of different
sizes acting in parallel to extract authentic vibrational features from
nonlinear background in noisy spectroscopic raw data. We test our approach by
retrieving asymmetric peaks in stimulated Raman spectroscopy (SRS), an ideal
test-bed due to its intrinsic complex spectral features combined with a strong
background signal. By using a theoretical perturbative toolbox, we efficiently
train the network with simulated datasets resembling the statistical properties
and lineshapes of the experimental spectra. The developed algorithm is
successfully applied to experimental data to obtain noise- and background-free
SRS spectra of organic molecules and prototypical heme proteins.
