Conventional methods for noise attenuation may cause some leakage of signal energy in the noise section as a result of incorrect parameter selection or inadequacy of denoising assumptions. We have shown that it is possible to retrieve the leakage energy by applying a weighting operator to the initial signal and adding the retrieved signal energy to the initially denoised data to obtain the final denoised data. In order to design an optimized weighting operator, we introduce a new local attribute, called local orthogonalization weight (LOW). LOW can be obtained by solving a least-square minimization problem using shaping regularization with a smoothness constraint. The proposed denoising approach corresponds to locally orthogonalizing signal and noise. Once the initial signal and noise models are given, the proposed approach can help retrieve the residual signal in the noise section. The local orthogonalization approach to random noise attenuation is applicable to processing of blended simultaneous-source seismic data, in which the preservation of useful signal is particularly important. Although the examples were 2-D, the method applies equally well in 3-D and in any other number of dimensions.
Random noise attenuation using local signal-and-noise orthogonalization
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