Residualbased localization and quantification of peaks in xray diffractograms
Abstract
We consider data consisting of photon counts of diffracted xray 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 denoising data of this kind do not explicitly take into account the modality of the final estimate. The residualbased procedure we propose uses the socalled 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.3687
 Bibcode:
 2007arXiv0711.3687D
 Keywords:

 Statistics  Applications
 EPrint:
 Published in at http://dx.doi.org/10.1214/08AOAS181 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)