Cultural Heritage Applications: Archaeological Ceramics and Building Restoration - On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling - page 143

Fig. 6.6 Ultrasound inspection at the dome

put together in a representation of the measurement point versus the signal
parameter evolution. Figure 6.6 shows different points of a B-Scan measured by
ultrasound at the dome.
The following sections describe: the ICA model of the problem; the performed
experiments, including the equipment setup; a comparison between the B-Scans
that were obtained with and without ICA as a pre-processor; and an analysis of the
sensitivity to detect interferences.

6.2.2 ICA Statement of the Problem

The recorded signals are modelled as the superposition of the backscattered signal
plus sinusoidal phenomena. This sinusoidal contribution should be determined in
order to know whether or not it is due to useful information about the material
structure such as material resonances, or whether it is due to interferences from the
instrumentation during measurement. The ICA statement of the problem is:

x k ð t Þ¼ s k ð t Þþ X

N 1

a ik e j ð x i t þ h ik Þ K ¼ 1...M ð 6 : 5 Þ

i 1

where M is the number of measurements, x k ð t Þ is the signal received from the
material at the position k of the B-Scan, s k ð t Þ is the backscattering signal that
depends a ik e j ð x i t þ h ik Þ on the material microstructure, and i ¼ 1...N 1 ;

k ¼ 1...M are the sinusoidal sources to be analyzed.