Image Processing Reference
In-Depth Information
electronic instrumentation) and 33.34% of coherent noise (accounting by “grain” noise
tied to material texture). Seven experiments were realized: 1 with time domain technique,
3 based on linear time-frequency decomposition using 2, 3 and 4 bands, and finally 3
utilising WVT with 2, 3 and 4 band again. The SNR after the 7 experiments were
measured. The results are exposed in Tables 1 and 2, together with the values expected
from expressions (3), (5) and (8).
In the first column of Tables 1 and 2, the initial SNR,
SNR
ini
of the ultrasonic traces are
shown. The experiment 1 in the Table 1 was planned in order to measure the behaviour of
the 2D time-combination method in terms of
SNR
2Dtime
improvement. The experiments
number 2, 3 and 4 had as objective to evaluate the accuracy of the expression
SNR
2DTFlinear
corresponding with the linear time-frequency combination. The difference among these 3
cases is the number of bands utilized [parameter
L
in expression (5)]; thus, the
experiments 2, 3 and 4 were performed with 2, 3 and 4 bands respectively. The particular
linear time-frequency transform used in these latter experiments was the undecimated
wavelet packet transform, (Mallat 1989, Shensa 1992, Coifman and Wickerhauser 1992),
with Daubechies 4 as mother wavelet, as it was used in the work (Rodríguez et al 2004b)
but with some new adjusts included in this case, which provide a better agreement (as it
can be seen in Table 1) between estimated and measured expressions of
SNR
2DTFlinear
that
in the mentioned work.
Finally, experiments 5 to 7 in Table 2 show the improvements obtained by using the WVT
transform in the combination. The differences among these 3 WVT experiments are again
the number of bands being involved: 2, 3 or 4, respectively. The SNR related to these 7
experiments are presented in Table 1 and Table 2. The expected SNRs estimated from their
theoretic expressions, together with the measured SNRs, are detailed for each case. The
measured SNR values, which are shown in these tables, were calculated as the mean of
different 10.000 SNRs obtained for each set of simulated traces.
SNR
2DTFlinear
(dB)
SNR
2Dtime
(dB)
experiment 1
SNR
ini
(dB)
4 bands
experiment 4
Est. Meas. Est. Meas. Est. Meas. Est. Meas.
0 0 0.11 0 0.34 0 0.05 0 0.75
1 2 2.08 4 3.53 6 5.72 8 8.81
2 4 4.07 8 7.62 12 11.54 16 16.63
3 6 6.06 12 11.46 18 17.53 24 24.57
4 8 8.11 16 15.42 24 23.41 32 32.26
5 10 9.97 20 19.39 30 29.34 40 40.44
6 12 12.01 24 23.43 36 35.28 48 48.42
7 14 14.11 28 27.38 42 41.23 56 56.24
8 16 16.13 32 31.34 48 47.31 64 64.25
9 18 18.16 36 35.32 54 53.24 72 72.17
10 20 20.08 40 39.33 60 59.27 80 80.43
Table 1. SNRs of the 2D representations obtained by means of the experiments 1 to 4.
2 bands
experiment 2
3 bands
experiment 3
