Savitzky-Golay Second Derivative Research Articles

Satellite Imagery for Monitoring and Mapping Soil Chromium Pollution in a Mine Waste Dump

Weathering and oxidation of sulphide minerals in mine wastes release toxic elements in surrounding environments. As an alternative to traditional sampling and chemical analysis methods, the capability of proximal and remote sensing techniques was investigated in this study to predict Chromium (Cr) concentration in 120 soil samples collected from a dumpsite in Sarcheshmeh copper mine, Iran. The samples’ mineralogy and Cr concentration were determined and were then subjected to laboratory reflectance spectroscopy in the range of Visible–Near Infrared–Shortwave Infrared (VNIR–SWIR: 350–2500 nm). The raw spectra were pre-processed using Savitzky-Golay First-Derivative (SG-FD) and Savitzky-Golay Second-Derivative (SG-SD) algorithms. The important wavelengths were determined using Partial Least Squares Regression (PLSR) coefficients and Genetic Algorithm (GA). Artificial Neural Networks (ANN), Stepwise Multiple Linear Regression (SMLR) and PLSR data mining methods were applied to the selected spectral variables to assess Cr concentration. The developed models were then applied to the selected bands of Aster, Hyperion, Sentinel-2A, and Landsat 8-OLI satellite images of the area. Afterwards, rasters obtained from the best prediction model were segmented using a binary fitness function. According to the outputs of the laboratory reflectance spectroscopy, the highest prediction accuracy was obtained using ANN applied to the SD pre-processed spectra with R2 = 0.91, RMSE = 8.73 mg/kg and RPD = 2.76. SD-ANN also showed an acceptable performance on mapping the spatial distribution of Cr using the ordinary kriging technique. Using satellite images, SD-SMLR provided the best prediction models with R2 values of 0.61 and 0.53 for Hyperion and Sentinel-2A, respectively. This led to the higher visual similarity of the segmented Hyperion and Sentinel-2A images with the Cr distribution map. This study’s findings indicated that applying the best prediction models obtained by spectroscopy to the selected wavebands of Hyperion and Sentinel-2A satellite imagery could be considered a promising technique for rapid, cost-effective and eco-friendly assessment of Cr concentration in highly heterogeneous mining areas.

Modeling the Raman spectrum of graphitic material in rock samples with fluorescence backgrounds: accuracy of fitting and uncertainty estimation.

We propose a robust technique called Savitzky-Golay second-derivative (SGSD) fitting for modeling the in situ Raman spectrum of graphitic materials in rock samples such as carbonaceous chondrite meteorites. In contrast to non-derivative techniques, with assumed locally linear or nth-order polynomial fluorescence backgrounds, SGSD produces consistently good fits of spectra with variable background fluorescence of any slowly varying form, without fitting or subtracting the background. In combination with a Monte Carlo technique, SGSD calculates Raman parameters (such as peak width and intensity) with robust uncertainties. To explain why SGSD fitting is more accurate, we compare how different background subtraction techniques model the background fluorescence with the wide and overlapping peaks present in a real Raman spectrum of carbonaceous material. Then, the utility of SGSD is demonstrated with a set of real and simulated data compared to commonly used linear background techniques. Researchers may find the SGSD technique useful if their spectra contain intense background interference with unknown functional form or wide overlapping peaks, and when the uncertainty of the spectral data is not well understood.

Enhanced Chemical Classification of Raman Images in the Presence of Strong Fluorescence Interference

Raman spectra and spectral images containing severe fluorescence interference are analyzed by using a variety of correlation and classification algorithms, both before and after preprocessing with the use of the Savitzky-Golay second-derivative (SGSD) method (and other related methods). Spectral correlation coefficient, principal component, and minimum Euclidean distance analyses demonstrate superior suppression of background and noise interference in Raman spectra when using SGSD preprocessing. The tested spectra include fluorescence interference that is more intense than the Raman features of interest and also contains broad background peaks that vary in shape and intensity from sample to sample. The high chemical information content of the SGSD-processed Raman spectra is demonstrated by using quantitative comparisons of correlation coefficients in a series of synthetic Raman spectra with either different or identical large backgrounds. The practical utility of SGSD in chemical image classification is illustrated by using an experimental Raman image of sugar microcrystals on substrates with large interfering background signals. The functional equivalence of SGSD and other windowed preprocessing algorithms is discussed.