Premium
Smoothing of X‐ray diffraction data and K α 2 elimination using penalized likelihood and the composite link model
Author(s) -
de Rooi Johan J.,
van der Pers Niek M.,
Hendrikx Ruud W. A.,
Delhez Rob,
Böttger Amarante J.,
Eilers Paul H. C.
Publication year - 2014
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576714005809
Subject(s) - smoothing , poisson distribution , distortion (music) , algorithm , measure (data warehouse) , diffraction , series (stratigraphy) , mathematics , quasi maximum likelihood , likelihood function , computer science , statistics , estimation theory , physics , optics , data mining , amplifier , computer network , bandwidth (computing) , paleontology , biology
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 α 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 α doublet the model is extended using the composite link model. As a result the data are decomposed into two smooth components: a K α 1 and a K α 2 part. For both smoothing and K α 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 α 2 stripping. The new method shows better results with less local distortion. Freely available software in MATLAB and R has been developed.