Nonlinear structure-enhancing filtering using plane-wave prediction |

The similarity-mean filter is a nonlinear filter that uses local
correlation coefficients as desired weight coefficients
(Liu et al., 2009a). It is described in Appendix A. We chose
the shaping operator with smoothing radius of samples in time to
calculate local similarity coefficients between the predicted data at
each prediction step and original data (reference
data). Figure 2a
displays similarity-weight coefficients from local correlation. The
elements with the shortest prediction distance get largest weights
because they provide the most accurate prediction and therefore are
most similar to the original image. We used zero-value boundary
conditions for the prediction, so the predicted amplitudes from the
left most and the right most sides are zero. This results in the
similarity coefficients on the corners of the weight cube to be
zero. In the weighted mean filter, large weight coefficients get
selected when the similarity is strong between processed data and
reference data. We introduce additionally Gaussian weights to localize
the smoothing characteristics of the filter

weight01,weightcube1,pwdatacube,wdatacube
Similarity
weights (a), product of Gaussian
weights and similarity weights (b), the data
only with similarity weights applied (c), and the
data with Gaussian similarity weights applied
(d).
Figure 2. |
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For comparison, we used the standard mean filter to process the prediction data volume (Figure 1d) along the prediction direction. The result is shown in Figure 3a and corresponds, in this case, to simple box smoothing along the local image structure. The standard mean filter simply stacks all information along the prediction direction. It enhances structural continuity but smears information across the fault.

For further discussion, we show the difference between the noisy image (Figure 1b) and structure-enhancing results with the standard mean filter and the Gaussian similarity-mean filter (Figure 3a and 3b). We kept the same scale of magnitude and plotting clips as that of the input image. From Figure 4a and 4b, the coherent events are well protected by the two methods because structure prediction can exactly predict coherent information. However fault information is destroyed by the mean filter (Figure 4a), while the similarity-mean filter provides a result where fault information is protected well, whereas random noise is attenuated (Figure 4b).

mean1,gsimilarstack1,mf,median1
Structure-enhancing
results using different methods. Standard mean
filtering (a), similarity-mean filtering (b),
standard median filtering with filter-window length
(c), and lower-upper-middle (LUM)
filtering with parameters (d).
Figure 3. |
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Nonlinear structure-enhancing filtering using plane-wave prediction |

2013-07-26