The Annals of Applied Statistics

Residual-based localization and quantification of peaks in X-ray diffractograms

P. L. Davies, U. Gather, M. Meise, D. Mergel, and T. Mildenberger

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Abstract

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.

Article information

Source
Ann. Appl. Stat. Volume 2, Number 3 (2008), 861-886.

Dates
First available: 13 October 2008

Permanent link to this document
http://projecteuclid.org/euclid.aoas/1223908044

Digital Object Identifier
doi:10.1214/08-AOAS181

Zentralblatt MATH identifier
1149.62102

Mathematical Reviews number (MathSciNet)
MR2516797

Citation

Davies, P. L.; Gather, U.; Meise, M.; Mergel, D.; Mildenberger, T. Residual-based localization and quantification of peaks in X-ray diffractograms. The Annals of Applied Statistics 2 (2008), no. 3, 861--886. doi:10.1214/08-AOAS181. http://projecteuclid.org/euclid.aoas/1223908044.


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