Source: Ann. Appl. Stat.
Volume 2, Number 3
We consider data consisting of photon counts of diffracted x-ray
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 de-noising data of this kind do not
explicitly take into account the modality of the final estimate.
The residual-based procedure we propose uses 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
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