Fast hyperparameter-free spectral approach for 2D seismic data reconstruction

Reconstruction of missing seismic data is a critical procedure for subsequent applications like multiple wave suppression, wave-equation migration imaging and so on. In this paper, a fast, hyperparameter-free and sparse iterative spectral estimation approach is proposed for the reconstruction of two-dimensional seismic data of randomly missing traces. The proposed approach is based on the harmonic structure of the frequency slice of seismic data and the weighted covariance fitting criterion. Specifically, the method first iteratively estimates the spectrum of the frequency slice by solving a weighted covariance fitting problem. Then, the missing data is reconstructed by using the estimated spectrum and a linear minimum mean-squared error estimator. However, the spectral estimation depends on matrix-vector multiplications for each iteration, which has a high computational cost when the data increase to a large size. To solve this problem, a fast iterative technology is proposed by using an inverse fast Fourier transform, which fully exploits the Hermitian–Toeplitz structure of the covariance matrix and the exponential form of the steering vector and it significantly reduces the computational complexity. The proposed algorithm is hyperparameter-free, can provide super spectral resolution, and thus obtain better reconstruction performance. The experimental results of synthetic and real seismic data show that the proposed algorithm has higher reconstruction accuracy and lower computational complexity compared to other commonly used reconstruction algorithms.