Research On The Neural Network Implementation Method Of Sparse Representation Of Seismic Data

Sparse representation theory is widely used in seismic data processing.Most of the representation methods have a unified mathematical model.Usually,by adding regularization constraints to improve the convergence effect of sparse optimization,the results show sparsity.L₀norm,as the best method of sparsity measurement,is difficult to be solved directly because of its non-convexity.In practice,L₁norm is often used to approach L₀norm.As one of the typical sparse representation problems,the sparse inversion of Radon transform focuses on two aspects:on the one hand,Radon transform is facing the bottleneck of resolution improvement.Since Radon operator matrix is a fixed basis function with large correlation,the theory of Compressed Sensing proves that under the basis function with large correlation,the traditional high-resolution iterative convex optimization method cannot converge to the optimal resolution.On the other hand,because of the inevitable large-scale matrix operation in the iterative convex optimization process of Radon transform,the current iterative convex optimization method has many iterations and low efficiency.In this paper,a neural network sparse optimization method based on the idea of Iterative Shrinkage and Threshold Algorithm(ISTA)is studied.The Learned Iterative Shrinkage and Threshold Method Algorithm(LISTA)transforms the single iteration of ISTA into a single-layer network,takes the basis function of Radon transform as the network learning parameter,inputs the seismic data in frequency domain and trains the network with unsupervised learning method,so as to realize the end-to-end mapping model of seismic data and Radon domain coefficient,and obtain the sparse solution of Radon inversion.By testing the Analog data models at different sampling points,it is proved that the correlation of Radon basis function after training by LISTA is decreased.Compared with traditional ISTA,the sparse optimization Radon coefficient resolution of this method is higher in less iterations,the calculation efficiency is obviously improved,and the convergence speed is faster.In the application of real seismic data,the feasibility of this method is verified.