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

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  • Davies, P. Laurie
  • Meise, Monika
  • Mergel, D.
  • Mildenberger, Thoralf

Abstract

We consider data consisting of photon counts of diffracted X-rays 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 procedure we propose is based on 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.

Suggested Citation

  • Davies, P. Laurie & Meise, Monika & Mergel, D. & Mildenberger, Thoralf, 2007. "Residual based localisation and quantification of peaks in X-ray diffractograms," Technical Reports 2007,23, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200723
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    References listed on IDEAS

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    1. Meise, Monika & Davies, Paul Lyndon, 2005. "Approximating data with weighted smoothing splines," Technical Reports 2005,48, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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    1. Davies, P. Laurie & Kovac, Arne & Meise, Monika, 2007. "Confidence sets and non-parametric regression," Technical Reports 2007,13, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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