Simultaneous Seismic Data Interpolation and Denoising Based on Nonsubsampled Contourlet Transform Integrating With Two-Step Iterative Log Thresholding Algorithm

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.