Structure Dictionary Learning And Its Applications In Seismic Data Processing

Dictionary learning is an adaptive sparse representation method,which is widely used in seismic data denoising,interpolation and sparse representation.Compared with the traditional sparse transform methods,the dictionary learned by the dictionary learning method contains the information of the data and can represent the seismic data more sparsely.However,in the current dictionary learning method,the training data patch vectorization is combined into new training data,and the vectorization destroys the structural features of the data.In order to overcome the above problems,we studied the dictionary learning methods based on graph regularization,structure graph dictionary learning method and Kronecker data driven tight frame method,and their application in seismic data denoising and interpolation.The details are shown as follows:Firstly,based on the local and non-local similarity of seismic data,a graph regularization dictionary learning model is established.According to the similarity of training data patches,we proposes two tree structure dictionary learning methods FDC and SDC.These two dictionary learning methods are simple,fast and the learned dictionary is adaptive.The numerical results show that the two tree structure dictionary learning methods based on graph regularization are better than the traditional sparse transform method.Then,based on the non-Gaussian property of seismic data,this paper uses the Gaussian mixed-scale model to simulate the non-Gaussian seismic signal.The dictionary atom in the Gaussian mixed-scale model is learned from the training data,but the training data contains noise,so that the learned dictionary atoms contain noise information.In order to ensure the effective data information in the atom,this paper proposes a graph structure dictionary learning method,which uses graph regularization to remove the noise information in the atom,so that the dictionary atom learned from the training data contains more effective seismic data information.In the numerical results section,the synthetic seismic data and the field seismic data are tested.The denoising results show that the graph structure dictionary learning method can preserve the information of seismic event while removing noise.Finally,for the high-dimensional seismic data,we propose the Kronecker data driven tight frame method(KronTF)and the directional data-driven tight frame with Kronecker structure(KronTFD).These two methods use tensor to avoid high-dimensional data vectorization and protect the structural characteristics of the data.Meanwhile,we propose a cyclic shift operator,so that the dictionary atom learned by the KronTFD method contains features in different directions of the data.The numerical results show that these two dictionary learning methods can better protect the structural characteristics of data while dealing with the denoising and interpolation of 2D and 3D seismic data.When the tested data contains multiple features in different directions,the KronTFD method and Data Driven tight frame method(DDTF)outperform the KronTF method.