Denoising scheme based on singular-value decomposition for one-dimensional spectra and its application in precision storage-ring mass spectrometry

Abstract: This work concerns noise reduction for one-dimensional spectra in the case that the signal is corrupted by an additive white noise. The proposed method starts with mapping the noisy spectrum to a partial circulant matrix. In virtue of singular-value decomposition of the matrix, components belonging to the signal are determined by inspecting the total variations of left singular vectors. Afterwards, a smoothed spectrum is reconstructed from the low-rank approximation of the matrix consisting of the signal components only. The denoising effect of the proposed method is shown to be highly competitive among other existing nonparametric methods, including moving average, wavelet shrinkage, and total variation. Furthermore, its applicable scenarios in precision storage-ring mass spectrometry are demonstrated to be rather diverse and appealing.