Residual-based localization and quantification of peaks in X-ray diffractograms. (English) Zbl 1149.62102

Summary: We consider data consisting of photon counts of diffracted X-ray radiation as a function of the angle of diffraction. The problem is to determine the positions, powers and shapes of the relevant peaks. An additional difficulty is that the power of the peaks is to be measured from a baseline which itself must be identified. Most methods of de-noising data of this kind do not explicitly take into account the modality of the final estimate.
The residual-based procedure we propose uses the so-called taut string method, which minimizes the number of peaks subject to a tube constraint on the integrated data. The baseline is identified by combining the result of the taut string with an estimate of the first derivative of the baseline obtained using a weighted smoothing spline. Finally, each individual peak is expressed as the finite sum of kernels chosen from a parametric family.


62P35 Applications of statistics to physics
82D99 Applications of statistical mechanics to specific types of physical systems
82D25 Statistical mechanics of crystals
62G08 Nonparametric regression and quantile regression
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