Image Processing Reference
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using a 2D product operator. The SNR was used as a quality index to evaluate both
methods; and the resulting evaluation data showed a better performance of the product
operator. Nevertheless, their performances were limited in both cases by the time
representation of the signals.
A technique in this same line that introduces the combination in the time-frequency domain,
based on the Wigner-Ville transform (WVT), was preliminary applied in (Rodríguez 2003).
This technique took into account the temporal and the frequency information of the
ultrasonic traces. A better SNR result than with the time domain method (Rodríguez et al
2004) was obtained. But this option presented two drawbacks: a lost of linearity of the
processed signals and a high computational cost.
In (Rodríguez et al 2004b) a new method was presented, performing the combination in the
time-frequency domain with a low computational cost by the use of a linear transform
(based on the wavelet transform (Daubechies 1992); its 2D SNR performance seemed to be
closed to that obtained in (Rodríguez 2003) with Wigner-Ville transforms.
The present chapter summarizes these three combination techniques previously proposed
by the authors for flaw detection from perpendicular transducers. A comparative analysis
(based on theoretic and experimental results) of their performances over a common set of
specific experiments is made. The objective is to establish the respective advantages and
inconveniences of each technique in a rather rigorous frame. For experimental evaluations,
we have arranged an ultrasonic prototype to generate (from 2 planes) ultrasonic near-field
beams collimated along the inspected piece, and to acquire the echoes from the transducers
involved in our experiments. The different combination results calculated in each case, from
the measured echo-responses, will be discussed.
3. Description of processing techniques for combination. Expressions of
SNR
A number of distinct combination techniques to fuse several ultrasonic traces, coming from
perpendicular transducers, have been proposed by the authors. There are two important
parameters that define all these techniques: a) the initial type of the traces representation,
and b) the particular operator utilized in their combination process.
To choose the best representation for the processing of signals is an open general problem
with multiples solutions; the two most popular representations are in time or in frequency
domains: a) the direct time domain is very useful for NDE problems because the spatial
localization of possible defects or flaws (in the material under testing) is closely related with
the apparition time of the echoes; b) the frequency domain is less used in this type of
ultrasound based applications because does not permit a spatial localization; in addition, the
spectrum of the ultrasonic information with interest for testing in some industrial
applications, is almost coincident with the mean spectrum of the “grain” noise originated
from the material texture, which some times appears corrupting the signals waveforms
associated to the investigated reflectors.
An interesting possibility for introducing spectral information in these applications is the
use of time-frequency representations (Cohen 1995) for the echo-graphic signals. This option
shows in a 2D format the time information for the different frequency bands in which the
received ultrasonic signals range. Therefore, each point of a 2D time-frequency
representation corresponds with one spectral frequency and with one time instant. Two
different time-frequency techniques, the wavelet transform (Daubechies 1992, Shensa 1992)
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