Open Access
September 2008 Residual-based localization and quantification of peaks in X-ray diffractograms
P. L. Davies, U. Gather, M. Meise, D. Mergel, T. Mildenberger
Ann. Appl. Stat. 2(3): 861-886 (September 2008). DOI: 10.1214/08-AOAS181


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.


Download Citation

P. L. Davies. U. Gather. M. Meise. D. Mergel. T. Mildenberger. "Residual-based localization and quantification of peaks in X-ray diffractograms." Ann. Appl. Stat. 2 (3) 861 - 886, September 2008.


Published: September 2008
First available in Project Euclid: 13 October 2008

zbMATH: 1149.62102
MathSciNet: MR2516797
Digital Object Identifier: 10.1214/08-AOAS181

Keywords: Confidence regions , Nonparametric regression , peak detection , thin film physics , x-ray diffractometry

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.2 • No. 3 • September 2008
Back to Top