title: Automated estimation of white Gaussian noise level in a spectrum with or without spike noise using a spectral shifting technique.
abstract: Various tasks, for example, the determination of signal-to-noise ratios, require the estimation of noise levels in a spectrum. This is generally accomplished by calculating the standard deviation of manually chosen points in a region of the spectrum that has a flat baseline and is otherwise devoid of artifacts and signal peaks. However, an automated procedure has the advantage of being faster and operator-independent. In principle, automated noise estimation in a single spectrum can be carried out by taking that spectrum, shifting a copy thereof by one channel, and subtracting the shifted spectrum from the original spectrum. This leads to an addition of independent noise and a reduction of slowly varying features such as baselines and signal peaks; hence, noise can be more readily determined from the difference spectrum. We demonstrate this technique and a spike-discrimination variant on white Gaussian noise, in the presence and absence of spike noise, and show that highly accurate results can be obtained on a series of simulated Raman spectra and consistent results obtained on real-world Raman spectra. Furthermore, the method can be easily adapted to accommodate heteroscedastic noise.
authors.affiliation: Michael Smith Laboratories, The University of British Columbia, 2185 East Mall, Vancouver, BC, Canada, V6T 1Z4.
authors.forename: H Georg
authors.initials: HG
authors.lastname: Schulze
authors.forename: Marcia M L
authors.initials: MM
authors.lastname: Yu
authors.forename: Christopher J
authors.initials: CJ
authors.lastname: Addison
authors.forename: Michael W
authors.initials: MW
authors.lastname: Blades
authors.forename: Robin F B
authors.initials: RF
authors.lastname: Turner