Raman signal extraction from CARS spectra using a learned-matrix representation of the discrete Hilbert transform

Removing distortions in coherent anti-Stokes Raman scattering (CARS) spectra due to interference with the nonresonant background (NRB) is vital for quantitative analysis. Popular computational approaches, the Kramers-Kronig relation and the maximum entropy method, have demonstrated success but may generate significant errors due to peaks that extend in any part beyond the recording window. In this work, we present a learned matrix approach to the discrete Hilbert transform that is easy to implement, fast, and dramatically improves accuracy of Raman retrieval using the Kramers-Kronig approach.