Comparison of Algorithms for Baseline Correction of LIBS Spectra for Quantifying Total Carbon in Brazilian Soils

LIBS is a promising and versatile technique for multi-element analysis that usually takes less than a minute and requires minimal sample preparation and no reagents. Despite the recent advances in elemental quantification, the LIBS still faces issues regarding the baseline produced by background radiation, which adds non-linear interference to the emission lines. In order to create a calibration model to quantify elements using LIBS spectra, the baseline has to be properly corrected. In this paper, we compared the performance of three filters to remove random noise and five methods to correct the baseline of LIBS spectra for the quantification of total carbon in soil samples. All combinations of filters and methods were tested, and their parameters were optimized to result in the best correlation between the corrected spectra and the carbon content in a training sample set. Then all combinations with the optimized parameters were compared with a separate test sample set. A combination of Savitzky-Golay filter and 4S Peak Filling method resulted in the best correction: Pearson's correlation coefficient of 0.93 with root mean square error of 0.21. The result was better than using a linear regression model with the carbon emission line 193.04 nm (correlation of 0.91 with error of 0.26). The procedure proposed here opens a new possibility to correct the baseline of LIBS spectra and to create multivariate methods based on the a given spectral range.Comment: 13 pages, 5 figure

Learning Co-Sparse Analysis Operators with Separable Structures

In the co-sparse analysis model a set of filters is applied to a signal out of the signal class of interest yielding sparse filter responses. As such, it may serve as a prior in inverse problems, or for structural analysis of signals that are known to belong to the signal class. The more the model is adapted to the class, the more reliable it is for these purposes. The task of learning such operators for a given class is therefore a crucial problem. In many applications, it is also required that the filter responses are obtained in a timely manner, which can be achieved by filters with a separable structure. Not only can operators of this sort be efficiently used for computing the filter responses, but they also have the advantage that less training samples are required to obtain a reliable estimate of the operator. The first contribution of this work is to give theoretical evidence for this claim by providing an upper bound for the sample complexity of the learning process. The second is a stochastic gradient descent (SGD) method designed to learn an analysis operator with separable structures, which includes a novel and efficient step size selection rule. Numerical experiments are provided that link the sample complexity to the convergence speed of the SGD algorithm.Comment: 11 pages double column, 4 figures, 3 table

Evolving Spatially Aggregated Features from Satellite Imagery for Regional Modeling

Satellite imagery and remote sensing provide explanatory variables at relatively high resolutions for modeling geospatial phenomena, yet regional summaries are often desirable for analysis and actionable insight. In this paper, we propose a novel method of inducing spatial aggregations as a component of the machine learning process, yielding regional model features whose construction is driven by model prediction performance rather than prior assumptions. Our results demonstrate that Genetic Programming is particularly well suited to this type of feature construction because it can automatically synthesize appropriate aggregations, as well as better incorporate them into predictive models compared to other regression methods we tested. In our experiments we consider a specific problem instance and real-world dataset relevant to predicting snow properties in high-mountain Asia