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.

A Fast, Automated, Polynomial-Based Cosmic Ray Spike–Removal Method for the High-Throughput Processing of Raman Spectra

“…24 This threshold therefore is unlike the polynomial order- and filter-window specifications, wherein no such direct relationship between the specified values and an accepted convention based on well-established methodologies exist. In addition, the noise standard deviation in a spectrum (and, by implication, in a profile) can be determined automatically; 25 thus, in principle, no user input is required. In practice however, the threshold can be adjusted if the default threshold is unsatisfactory.…”

Automatic Baseline Subtraction of Vibrational Spectra Using Minima Identification and Discrimination via Adaptive, Least-Squares Thresholding

“…In this respect, the present procedure falls short of the strictest definition of baseline correction in the sense that all spectra, tested or hypothetical, are shifted upward by approximately one-half the peak-to-peak (p-p) noise level. A supplemental modification to the present work would involve employing an automated estimation of noise level and further correction of the vertical offset in the manner of Schultze et al 24…”

A Two-Dimensionally Coincident Second Difference Cosmic Ray Spike Removal Method for the Fully Automated Processing of Raman Spectra

“…Although more false positives could be expected by using this lower threshold, their occurrences were countered by the requirement of being coincident. We used a fully automated method 22 to determine the noise standard deviation in spectra.…”