Raman signal extraction from BCARS intensity measurements using deep learning with a prior excitation proﬁle

. Broadband Coherent anti-Stokes Raman Scattering (BCARS) microscopy is a useful technique for chemical analysis and allows the full vibrational ﬁngerprint spectrum of a specimen to be obtained in millisec-onds. A major drawback to this technique is the presence of the non-resonant background response producing interference which prevents classical spectral analysis of the sample. Using a convolutional autoencoder and measurements of the laser characteristics, we have shown that it is possible to remove this background without requiring supervision, as is typically required for conventional removal methods. This approach therefore simpliﬁes the analysis of hyperspectral images obtained with BCARS.


Introduction
Broadband Coherent Anti-Stokes Raman Scattering (BCARS) is an imaging technique that allows for labelfree visualization of chemical species.BCARS typically employs two ultrafast lasers that interact via the third order nonlinearity, generating a coherent signal that provides vibrational information.However, in BCARS, the generated signal is accompanied by a non-resonant background (NRB) that can obscure the molecular vibrational signal of interest.
The NRB arises from various sources, such as parametric frequency-independent processes.
The NRB can significantly affect the sensitivity and specificity of BCARS imaging, particularly in biological samples where the density of resonant oscillators can be small.To overcome the challenges posed by the NRB in BCARS, various techniques have been developed, including the use of polarization shaping [1], frequency modulation [2] and temporal methods [3].These techniques aim to enhance the signal-to-noise ratio of BCARS imaging by selectively suppressing the non-resonant background.
In our previous work, we trained an autoencoder to perform NRB removal, using no prior system characteristics in the approach [4].This technique had poor performance when the spectra were complex, because the network was trained on ideal spectra with a flat stimulation profile.In this work, we demonstrate the efficient removal of the NRB from BCARS measurements taken with our experimental system, through the incorporation of the lasers stimulation profile in the training and validation data of the network.

Phase retrieval 2.1 Conventional methods
In BCARS, typically the resonant χ (3) is sought as it provides Raman information.However, due to the NRB, there is no simple relation between the measured intensity and the resonant χ (3) .It has been shown that the Kramers-Kronig (KK) method allows quantitative and reliable extraction of the Raman spectrum of neat chemicals and tissues [5].However, the main drawback to the KK technique is the requirement of an NRB reference spectrum.If the measured NRB is not purely real due to absorbance or scattering, the retrieved Raman signal will also contain errors.The implementation of KK thus also requires baseline detrending to remove a phase-error term related to windowing and the NRB signal itself.This requires supervision through optimizing detrending parameters manually, as the error term varies between samples.

Deep learning methods
The deep learning approach to NRB removal is a useful alternative to conventional methods, since it is unsupervised and requires no reference measurement of the NRB in the sample.This has been demonstrated first by Valensise et al. [6] using purely synthetic BCARS data and a flat stimulation profile which was used to train a Convolutional Neural Network (CNN).
In our work, we used a convolutional autoencoder architecture, and trained it with pairs of BCARS spectra and its respective Raman spectrum.Starting from the BCARS polarization equation, we simulate a resonant susceptibility as a sum of Lorentzians, then model the NRB based on assumptions on its shape, we then incorporate the laser through a prior measurement of its spectrum and finally include extrinsic effects such as noise and scattering.This allows highly realistic training data to be fed to the network and thus the mapping between the susceptibility and the final measured response can be determined such that no further processing is required.

Network architecture
Our architecture, based on VECTOR [4], incorporates 18 convolutional layers and symmetric skip connections between paired convolutional and transposed convolutional layers in the encoder and decoder.Skip connections were shown to significantly improve performance for deeper networks like the one used in this paper.They function by allowing input features or shallow layer features to bypass the low-dimensional latent space, preserving highlevel features that might otherwise be lost.The loss function used was the mean absolute error between the CARS input and the underlying Raman signal.

Results
In Figure 1, we show four experimental BCARS spectra of samples obtained with our system.In Figure 2, we demonstrate the performance of our NRB removal method for the four chemical spectra, using the autoencoder network which was trained on simulated pure chemical spectra with a low number of sharp resonances, named VECTOR-MU-Chem.We show that the network performs well at recovering the Raman spectrum of the three plastic samples (PMMA, polystyrene, Polymer), however the baseline in the glycerol spectrum at 1300 cm -1 is flat, which is not the case in the Raman spectrum.We note that there is a tradeoff between the complexity of the retrieval, with the generalization performance, however our approach can be tailored to the sample of interest easily, through modification of simulation parameters.

Figure 1 .
Figure 1.Raw BCARS spectra of the four chemical samples used for testing the retrieval.Area right of th dashed line is scaled up by 10 times for clarity.

Figure 2 .
Figure 2. Retrieval of the four chemicals: (a) glycerol, (b) a proprietary polymer slide, (c) PMMA, (d) polystyrene in orange.The spectra are shown together with the corresponding intensity calibrated spontaneous Raman spectra in blue.