Image Processing Reference
In-Depth Information
with noise) are set to cero. For each frequency band, a combination is made by using the
2D product operator, like as it was used in the time-domain combination technique. The
final 2D representation is obtained with a point to point product of all the 2D displays
related to the different frequency bands. A functional scheme of this WVT based
combination method is presented in the Figure 3, for the case of eight transducers
considered in this section.
Fig. 3. Functional scheme of the WVT traces combination method.
A good estimation of the resulting SNR for the 2D representation in this WVT case,
SNR 2DWVT , can be obtained from the results presented in (Rodríguez 2003):
SNR
()3
dB

L SNR
()
dB
(8)
2
DWVT
ini
Therefore, the improvement factor of the SNR, expressed in dB, which can be obtained by
this WVT method, is the triple of the number of frequency bands that had been selected.
In consequence, the theoretic improvement levels in the SNR provided by the three
alternative techniques for combining ultrasonic traces coming from two perpendicular
transducers, (i.e., the basic option using traces envelope product, and the others two options
based on linear time-frequency and WVT trace decompositions), are quite different.
So, the quality of the resulting 2D combinations, in a SNR sense, is predicted to be quite
better when time-frequency decompositions are chosen, and the best results must be
expected for the Wigner-Ville option, which in general seems to be potentially the more
effective processing. Nevertheless, in spite of these good estimated results for the WVT case,
it must be noted that in general this option supposes higher computational cost. Therefore,
the more effective practical option should be decided in each NDE situation depending on
the particular requirements and limitations in performance and cost being needed. In the
following sections, the confirmation of these predictions will be carried out, by means of
several experiments from simulated and measured ultrasonic traces.
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