Smoothing of X-ray diffraction data and K alpha(2) elimination using penalized likelihood and the composite link model

Jacob Rooi, NM van der Pers, RWA Hendrikx, R Delhez, AJ Bottger, Paul Eilers

Research output: Contribution to journalArticleAcademicpeer-review

13 Citations (Scopus)


X-ray diffraction scans consist of series of counts; these numbers obey Poisson distributions with varying expected values. These scans are often smoothed and the K alpha(2) component is removed. This article proposes a framework in which both issues are treated. Penalized likelihood estimation is used to smooth the data. The penalty combines the Poisson log-likelihood and a measure for roughness based on ideas from generalized linear models. To remove the K alpha doublet the model is extended using the composite link model. As a result the data are decomposed into two smooth components: a K alpha(1) and a K alpha(2) part. For both smoothing and K alpha(2) removal, the weight of the applied penalty is optimized automatically. The proposed methods are applied to experimental data and compared with the Savitzky-Golay algorithm for smoothing and the Rachinger method for K alpha(2) stripping. The new method shows better results with less local distortion. Freely available software in MATLAB and R has been developed.
Original languageUndefined/Unknown
Pages (from-to)852-860
Number of pages9
JournalJournal of Applied Crystallography
Publication statusPublished - 2014

Research programs

  • EMC NIHES-01-66-01

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