Image Processing Reference
In-Depth Information
ultrasonic transducers (H1, H2, H3 and H4) with horizontal propagation beams and four
transducers (V1, V2, V3 and V4) with vertical propagation beams.
Some theoretical characterizations of this method, including statistical distributions of the
combined noise and some results about SRN enhancements were presented in (Rodríguez et
al 2004). The more important result of that work is the expression of the resulting SNR for
the 2D ultrasonic representation after the combination process.
The SNR of the initial traces,
SNR
ini
, containing an echo-pulse and noise, is defined as:
M
1
2
(())
p i
M
i
1
(1)
SNR
() 0 g
1
dB
ini
L
2
(())
ni
L
i
1
where,
p
denotes the echo-pulse and
n
represents the noise;
M
is the length of the pulse and
L
is the length of the whole ultrasonic trace.
The SNR of the final 2D representation is:
MM
1
2
(
p
( , ))
ij
2
D
2
M
i
11
j
SNR
() 0l g
1
dB
(2)
2
D
LL
2
(
ni j
( , ))
2
D
2
L
i
11
j
where,
p
2
D
and
n
2
D
denotes the 2D representation of the echo-pulse and of the grain noise;
M
and
L
are the dimensions of the 2D rectangular representations of the echo-pulse and of the
ultrasonic trace, respectively.
The SRN of the 2D representation obtained by using this time-domain combination method,
SNR
2Dtime
, can be expressed as a function of
SNR
ini
:
SNR
()2
dB
SNR
()
dB
(3)
2
Dtime
ini
In consequence, the resulting SNR with this method,
SNR
2Dtime
, expressed in dB, is the
double of the initial SNR of the A-scans before combination (
SNR
ini
).
3.2 Linear time-frequency combination technique
The time-domain traces combination, previously described, works without any frequency
consideration. In order to obtain a further improving of SNR, it would be necessary to use
some type of processing in the frequency domain. Nevertheless, the ultrasonic echoes
coming from flaws in some NDE applications, and the grain noise produced by the own
material structure, have similar global mean spectra, which difficult the flaw discrimination
in the frequency domain. But if these spectra are instantaneously analyzed, it can be
observed that the instantaneous spectrum is more regular for echo-signal than for grain
noise. The tools that permit the analysis of these differences between signal and noise are
the time-frequency representations, which can be obtained by using a linear or also a non-
linear transformation.
In this section, we will deal with the application of linear time-frequency representations to
improve our signal-combination purpose. The two most popular linear time-frequency
