SERS (surface-enhanced Raman scattering) enhances the Raman signals, but the plasmonic effects are sensitive to the chemical environment and the coupling between nanoparticles, resulting in large and variable backgrounds, which make signal matching and analyte identification highly challenging. Removing background is essential, but existing methods either cannot fit the strong fluctuation of the SERS spectrum or do not consider the spectra's shape change across time. Here we present a new statistical approach named SABARSI that overcomes these difficulties by combining information from multiple spectra. Further, after efficiently removing the background, we have developed the first automatic method, as a part of SABARSI, for detecting signals of molecules and matching signals corresponding to identical molecules. The superior efficiency and reproducibility of SABARSI are shown on two types of experimental datasets.