Seismic data interpolation and denoising play vital roles in obtaining complete and clean data in seismic data processing. Seismic data usually miss along various spatial axes and always mix with random noise. To obtain complete and clean seismic data, reconstruction technology can interpolate missing data and attenuate random noise. A nonsubsampled contourlet transform (NSCT) is an effective transform to obtain multiscale and multidirection sparse domain data for compression sensing interpolation and denoising. However, conventional iterative shrinkage/thresholding (IT) cannot handle ill-posed and ill-conditioned equations for solving linear inverse problem. We present a two-step iterative log thresholding (TwILT) method to overcome ill-posed and ill-conditioned problems and improve the convergence rate and solution accuracy, which can interpolate and denoise seismic data simultaneously in the NSCT framework. First, we use the NSCT to convert the seismic missing data with random noise to sparse domain. Then, we apply the TwILT algorithm to interpolate and denoise data in sparse domain. The result of each iteration is based on the results of the previous two iterations, which can accelerate convergence rate. In addition, log thresholding can further improve convergence rate and solution accuracy. Finally, we use inverse NSCT to obtain the interpolated and denoised seismic data. The new method can reconstruct the irregularly missing data and attenuate random noise to obtain complete and clean seismic data with high accuracy, which is crucial for seismic imaging and inversion. We demonstrate the applicability and effectiveness of this simultaneous interpolation and denoising technique with successful applications to both synthetic and field data examples.

中文翻译：

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基于非下采样Contourlet变换与两步迭代对数阈值算法相结合的同步地震数据插值和去噪

地震数据插值和去噪对于地震数据处理中获得完整、干净的数据起着至关重要的作用。地震数据通常会沿着各种空间轴丢失，并且总是与随机噪声混合。为了获得完整和干净的地震数据，重建技术可以对缺失的数据进行插值并衰减随机噪声。非下采样轮廓波变换 (NSCT) 是一种获得多尺度和多方向稀疏域数据的有效变换，用于压缩感知插值和去噪。然而，传统的迭代收缩/阈值 (IT) 无法处理用于求解线性逆问题的病态和病态方程。我们提出了一种两步迭代对数阈值（TwILT）方法来克服病态和病态问题并提高收敛速度和求解精度，它可以在NSCT框架中同时对地震数据进行插值和去噪。首先，我们使用 NSCT 将具有随机噪声的地震缺失数据转换为稀疏域。然后，我们应用 TwILT 算法对稀疏域中的数据进行插值和去噪。每次迭代的结果都是基于前两次迭代的结果，可以加快收敛速度​​。此外，对数阈值化可以进一步提高收敛速度和求解精度。最后，我们使用逆 NSCT 来获得插值和去噪的地震数据。新方法可以重构不规则缺失的数据，衰减随机噪声，获得完整、干净、高精度的地震数据，这对地震成像和反演至关重要。