The adaptive weighting operator can be applied to make the traditional rank-reduction method adaptive:
Symbols | Meanings |
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3D noisy seismic data |
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abbreviated notation of 2D frequency slice |
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block Hankel matrix |
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signal component |
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estimated signal component |
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left singular vector matrix |
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singular-value matrix |
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right singular vector matrix |
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weighting matrix |
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damping matrix |
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damping threshold matrix |
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temporary variable |
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D-transform |
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Hankelization operator |
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thresholding operator |
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averaging operator |
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rank |
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damping factor |
Tests | Noisy (dB) | RR (dB) | DRR (dB) | ODRR (dB) |
Linear synthetic (N=3) | -8.39 | 6.57 | 10.29 | 11.27 |
Linear synthetic (N=6) | -8.39 | 3.45 | 8.35 | 10.86 |
Hyperbolic synthetic (N=10) | -2.17 | 8.27 | 9.58 | 9.65 |
Hyperbolic synthetic (N=20) | -2.17 | 7.04 | 10.08 | 11.00 |
Tests | FK (s) | RR (s) | DRR (s) | ODRR (s) | ||
Linear synthetic (N=3) | 0.13 | 2.27 | 2.45 | 2.43 | ||
Linear synthetic (N=6) | 0.17 | 3.02 | 3.04 | 3.17 | ||
Hyperbolic synthetic (N=10) | 0.43 | 1.69 | 1.71 | 1.83 | ||
Hyperbolic synthetic (N=20) | 0.49 | 2.75 | 2.69 | 2.83 |