  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.
