EXPRESS: Enhanced SVD for Signal-Noise Separation in Spectroscopic Data

Singular Value Decomposition (SVD) is a primary tool for exploratory analysis and for separating signal from noise and background in spectroscopic data, but it does not account for baseline variation. Standard SVD can assign to baseline features singular values comparable in magnitude to those of genuine chemical components, obscuring the boundary between signal and noise in the singular value spectrum and complicating determination of the chemical rank. This Note describes a preprocessing-enhanced SVD algorithm in which a Fourier-domain first-derivative transformation is combined with weights derived from the noise present in the data before the decomposition is performed, suppressing baseline contributions without loss of true signal components. The abstract spectra and time-traces are returned to the original spectral and temporal domains by inverse transformation, and a sign-ambiguity resolution procedure based on correlation coefficients is included. The algorithm is demonstrated on both synthetic and experimental time-dependent FTIR spectroscopic data. Relative to standard SVD, the enhanced decomposition yields a flat noise floor beyond the retained components, confining the baseline contribution to the discarded subspace rather than dispersing it through the low-rank subspace, and the recovered abstract spectral and temporal vectors carry less baseline contamination. Although demonstrated with time-dependent FTIR data, the algorithm applies to any variable-dependent spectroscopic measurement that can be organized as a two-way matrix. The implementation is released as open-source software.