Raman Signal Extraction from CARS Spectra Using a Learned-Matrix Representation of the Discrete Hilbert Transform

TL;DR

This paper introduces a learned-matrix method for the discrete Hilbert transform that enhances the accuracy of Raman signal extraction from CARS spectra by effectively removing nonresonant background distortions.

Contribution

The paper proposes a novel learned-matrix approach to the discrete Hilbert transform, improving Raman signal retrieval accuracy over traditional methods.

Findings

Significantly reduces errors in Raman spectra analysis.

Faster and easier to implement than existing methods.

Improves quantitative analysis of CARS spectra.

Abstract

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.