Residual based localisation and quantification of peaks in X-ray diffractograms
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Date
2007-07-13T14:08:45Z
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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.
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Keywords
Diffracted X-ray, Peak, Taut string method, Weighted smoothing spline