Tensor Dictionary Learning And Its Application In Seismic Data Reconstruction

With the continuous improvement of the complexity and fineness of seismic exploration,as well as the popularization of two wide and one high acquisition technology,higher requirements are put forward for the quality of seismic data,but the lack of seismic data will be caused by various factors in the actual collection,so effective seismic data reconstruction technology is an important step in preprocessing.Sparse change has a good application effect in the field of seismic signal processing,and dictionary learning is different from the sparse change method of fixed basis function,and an adaptive overcomplete dictionary can be trained according to the data.Inspired by the classic K-SVD algorithm,combined with the Tucker decomposition of tensors,this paper generalizes the reconstruction of high-dimensional seismic data to tensor space,which can make full use of the spatial characteristics of high-dimensional data and improve the credibility of reconstruction.In terms of sparse representation,this paper uses the tensor-based orthogonal matching tracking algorithm(TOMP)to find the sparse coefficient tensor,and uses the alternating least squares algorithm(ALS)to update the dictionary tensor,and continuously iterates the optimal solution of the residual to train a suitable set of dictionary tensors and coefficient sparse tensors.Due to the good redundancy of seismic data,the missing data can be predicted according to the main characteristics of the observation data,and the reconstruction of seismic data can be realized.In the numerical simulation of three-dimensional seismic data and five-dimensional seismic data,the tensor dictionary learning algorithm(TDL)used in this paper achieves a good reconstruction effect in the recovery of missing data,which can maintain the continuity of the in-phase axis and the amplitude value of seismic waves,and also compares the reconstruction under different deletion rates,which verifies the practicability of the high-dimensional reconstruction algorithm in large-scale deletion.Since the existence of random noise is often mixed with in the reconstruction of actual seismic data,this paper also studies the simultaneous interpolation and denoising to verify that the TDL algorithm has good noise immunity while reconstructing.According to the comparison of the processing effect of actual seismic data,it shows that the method proposed in this paper has certain application prospects.