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Comparison between signal reliability based SVMF and signal energy based SVMF

Another criteria for selecting the variable window length $ L_{i,j}$ is by signal energy (SE), as introduced in the time-varying median filter (TVMF) framework (Liu et al., 2009):

$\displaystyle L_{i,j}=\left\{\begin{array}{ll} L+l_1,\quad 0\quad \le \vert e^L...
...L_{i,j}\vert < 2T\\ L-l_4,\quad \vert e^L_{i,j}\vert \ge 2T \end{array}\right.,$ (5)

where $ e^L_{i,j}$ is the signal energy (SE), which can be defined as the absolute value of the initially filtered data $ u^L_{i,j}$ with a window length $ L$ for point $ x_{i,j}$ . $ T$ is a threshold value, and can be calculated by:

$\displaystyle T=\frac{1}{N_x\times N_t}\sum_{i=1}^{N_x}\sum_{j=1}^{N_t} \vert e^L_{i,j}\vert.$ (6)

Here, $ N_x$ and $ N_t$ denote the number of spatial and temporal samples.

The SE based SVMF differs from the SR based SVMF in that the former uses SE as a reference to pick up useful signal while the latter uses SR to pick up useful signal. Figures 1a and 1b give a comparison between the normalized SR and SE maps for the synthetic example as shown in Figure 4. Figures 1c and 1d gives the corresponding filter length map. As we can see, the SE map has a higher resolution while SR map gives a smoother result. However, the SE map gives some "fake" points, as indicated by arrows. These "fake" points come from the remnant blending noise. Because the initial MF can not remove all the blending noise, some noise points will have large amplitude thus will be picked up by the SE criteria. These "fake" points may result in very short filter length even for noisy area, as indicated by the arrows in Figure 1d. Because of an embedded smoothing function when calculating the local similarity, those remnant noise points will be smoothed and thus show small amplitude in the SR map. The SR map can get much better result when the seismic profile contains some ambient random noise. Because the initial MF in the SVMF will harm the random ambient noise rather than removing them, the amplitude properties of random ambient noise can not be changed too much, but the similarity properties will be changed a lot. Figure 2 gives the comparison between SR and SE maps and their corresponding filter length maps after adding some ambient Gaussian white noise to the seismic data. In this case, the SR can still capture the useful events well while the SE can not. The corresponding variable filter length map thus gives a more plausible reference.

simi1 energy1 L1 L1-tsmf
simi1,energy1,L1,L1-tsmf
Figure 1.
(a) SR map and (b) SE map corresponding to the data shown in Figure 4. (c) Filter length map using SR. (d) Filter length map using SE.
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simi1-n energy1-n L1-n L1-tsmf-n
simi1-n,energy1-n,L1-n,L1-tsmf-n
Figure 2.
(a) SR map and (b) SE map for noisy data. (c) Filter length map using SR. (d) Filter length map using SE.
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next up previous [pdf]

Next: Implementation steps of SVMF Up: Method Previous: Space-varying median filter

2015-11-23