A High-Efficiency and Robust Compressive Sensing Reconstruction and Regularization Technique

Seismic data acquisition is a crucial procedure in seismic exploration. Compressive sensing (CS) is a new signal sampling framework and breaks through the limitation of Nyquist theorem (Donoho, 2006). The application of CS in seismic data acquisition (Mosher et al. 2012) can potentially improve exploration efficiency and lower costs. CS helps the reconstruction of seismic data before subsequent data processing stages. Numerous researchers have made contributions to the advancement of techniques for reconstructing regularly sampled data. The majority of these methods fall under the category of prediction error filter techniques (Li et al. 2017; Spitz 1991; Zheng et al. 2022), sparse transformation approaches (Fomel & Liu 2010; Gong et al. 2016), and low-rank constraint approaches (Sacchi 2009). In recent years, numerous deep learning-based reconstruction methods have been proposed (Chen et al. 2023; Liu & Ma 2024). These methods are often used to uniformly sampled data. In non-uniform sampling cases, the data are usually binning to a uniform grid. However, data binning ignores the actual positions of seismic traces, and compromises the continuity of seismic events. To address the challenges presented by the distortions and artifacts caused by the binning methods, researchers have explored non-uniform data processing methods using specialized non-uniform sampling transforms. Notable among these are non-uniform Fourier transform (Yu et al. 2020), and non-uniform curvelet transform (Zhang et al. 2019). Kumar et al. (2015) extended the matrix completeness to a non-uniform grid to conduct regularization of two-dimensional seismic data. Jiang et al. (2017) extended the traditional projection onto convex sets (POCS) approach (Abma & Kabir 2006) to the extended POCS (EPOCS), which incorporates an interpolation operator and broadens its applicability to arbitrary irregular acquisition. Carozzi & Sacchi (2021) modified the multi-singular spectrum analysis (MSSA) and proposed an interpolated MSSA (I-MSSA) algorithm, which is a reconstruction algorithm that honors real coordinates. Li et al. (2012) proposed a 2D seismic data reconstruction approach relying on compressed sensing interpolation. Yu et al. (2020) utilized non-uniform Fourier transform to map seismic data from uniform to non-uniform grids, and applied this approach for 3D seismic data reconstruction. Yu & Ma (2023) proposed a new combined sampling operator that can simultaneously perform non-uniform grid regularization and reconstruction of 3D seismic data. This method reconstructs 3D seismic data with a 2D barycentric Lagrangian (2DBL) interpolator (Berrut & Trefethen 2004), which significantly reduces the computational cost. In field seismic exploration, the sampled data may contain random and outlier noise. Outlier noise refers to values or signals in a dataset that significantly deviate from other data points (Osborne & Overbay 2019). These outliers may arise due to measurement errors, sensor malfunctions, environmental interference, or other abnormal conditions. Random noise refers to small, unpredictable changes scattered throughout the data, often due to minor factors like measurement errors. Numerous methods have been introduced to suppress the random noise in seismic data (Zeng et al. 2022). In seismic data processing, the identification and handling of outlier noise are crucial, as such noise can distort the characteristics of the actual seismic data. Zhao et al. (2018) proposed a robust curvelet thresholding approach by formulating an optimization problem using Huber norm regularization. Li et al. (2019) developed a POCS method enhanced with Huber- optimization for seismic data interpolation. Chen et al. (2022) developed a robust deep learning (DL) denoising approach for seismic data that operates in a self-supervised way without clean data. In the paper, a high-efficiency and robust seismic data reconstruction method based on fast sparse inversion is proposed. Compared with ISTA, the main highlight of the new method is the adoption of an accelerated iterative shrinkage threshold algorithm (AISTA) to improve the convergence speed and reconstruction accuracy. Considering the existence of the obstacle in field operation, a non-uniform interpolator operator is designed to alleviate the adverse influence to reconstruction accuracy. Moreover, 3D curvelet transform (Candes et al., 2004; Herrmann et al., 2008) is selected as sparse operator to boost the iterative convergence speed. In order to decrease the computational redundancy of 3D curvelet transform, a parallel patching strategy is utilized to segment a large volume of data into small patches, following to parallel-compute the 3D curvelet coefficient of each small patch to further improve the computational efficiency. Finally, we demonstrate the effectiveness of the proposed method by massive field datasets.