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 de-noising effect of the proposed method is shown to be highly competitive among other existing non-parametric 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.