Peak Detection in Mass Spectra: An Application of Least-Squares Piecewise Monotonic Approximation

Peak detection in mass spectrometry is a challenging signal-processing problem due to the presence of noise, overlapping peaks, and the intrinsic complexity of spectral data. This paper investigates the application of the least-squares piecewise monotonic approximation method to automatic peak detection in mass spectra. The method models the data as a sequence of alternating monotonic segments and identifies peaks through the optimal determination of turning points. The underlying optimization problem is combinatorial in nature, requiring to test a large number of possible breakpoint arrangements. However, because of a decomposition property of the approximation problem, the computation can be carried out efficiently through dynamic programming in quadratic time complexity. Within this approach, peak detection is formulated and solved as a globally optimized approximation problem under minimal assumptions. The method is applied to a complex mass spectrum from a publicly available MassBank record. Numerical results show that the method reliably identifies both dominant and subtle spectral features, while simultaneously capturing the underlying structure of the data stage by stage. The accuracy of the approximation improves consistently, remaining free of oscillatory artifacts, as the number of monotonic segments increases. The findings demonstrate that piecewise monotonic approximation gives a robust, accurate, and computationally efficient methodology for automatic peak detection in mass spectrometry.