Simultaneous seismic data de-aliasing and denoising with a fast adaptive method based on hybrid wavelet transform

Missing data and random noise are prevalent issues encountered during the processing of acquired seismic data. Interpolation and denoising represent economical solutions to address these limitations. Recovering regularly missing traces is challenging because of the spatial aliasing, and the extra difficulty is compounded by the presence of noise. Hence, developing an effective approach to realize denoising and anti-aliasing is important. Projection onto convex sets is an effective method for recovering missing seismic data that is typically used for processing data with a good signal-to-noise ratio. The computational attractiveness of the projection onto convex sets reconstruction approach is compromised by its slow convergence rate. In this study, we aimed to efficiently implement simultaneous seismic data de-aliasing and denoising. We combined a discrete wavelet transform with a seislet transform to construct a hybrid wavelet transform. A new fast adaptive method based on the fast projection onto convex sets method was proposed to recover the missing data and remove random noise. This approach adjusts the projection operator and iterative shrinkage threshold operator. The result is influenced by the threshold value. We enhanced the processing accuracy by adopting an optimal threshold strategy. Synthetic and field data tests indicate the effectiveness of the proposed method.