Reconstruction of missing seismic traces based on sparse dictionary learning and the optimization of measurement matrices

Abstract

Due to limitations arising under complicated geological conditions and field collection environments, we often cannot collect complete and regular field seismic data. To solve that problem, the reconstruction of seismic data has been widely studied. In this paper, we propose a reconstruction algorithm for seismic data with missing traces based on sparse dictionary learning and measurement matrix optimization. The algorithm views the seismic data as a matrix. It first uses the neighboring channel to fill in the missing trace and then uses the transposed matrix and applies the K-singular value decomposition (K-SVD) algorithm by columns to train the sample, obtaining an over-complete dictionary that can be used to develop an optimal sparse representation of seismic data. In the process of seismic data reconstruction, we first transpose the seismic data with missing traces, adopt the regularized orthogonal matching pursuit (ROMP) algorithm to obtain optimum estimations of the data in each column and then transpose the matrix to obtain the reconstructed seismic data. To further increase the quality of seismic data reconstructions, the algorithm presented in this paper also introduces the Equiangular Tight Frame (ETF) method to optimize the measurement matrix. The experiments indicate that this paper's algorithm can achieve high-quality reconstructions of seismic data.