Research On High Resolution Radon Transform Based On L₀ Norm

Radon transform is widely used in seismic data processing.Using the regularization constraints can improve the resolution of Radon transform and improve the processing results of seismic data.As an optimal method for measuring data sparsity,the research of L₀ norm in Radon transform has certain practical application value.It is difficult to directly get the solution because of the nonconvexity of the L₀norm.In this paper,two methods are proposed to approximate the L₀ norm respectively,so as to achieve the purpose of using L₀ norm to constrain the Radon transform.One method is to introduce the Smoothed L₀ Norm?SL₀?sparse constraint into Radon transform,which reduces the difficulty of solving the problem.That is to say,by constructing smoothed continuous functions to approximate the L₀ norm and used as the objective function of parabolic Radon transform.The optimal solution is obtained by the steepest descent method and the gradient projection principle.Experimental results of seismic data reconstruction applied to theoretical models and actual data show that the proposed method further improves the resolution of Radon transform,and better improves the continuity and AVO characteristics of missing seismic data.Another way is to use the matching pursuit?MP?algorithm to approximate the L₀norm,that is,selecting matching subspace according to the energy distribution of high-order Radon domain,which greatly improves the sparsity of Radon domain data.In thus small subspace,the high-order Radon transform is realized quickly to estimate the effective data.This method is applied to the separation of simultaneous source seismic data and a set of iterative algorithms are designed.Compared with the iterative reweight least square method?IRLS?,the experimental results of synthetic data and real data show that this method has higher signal-to-noise ratio and better denoising effect.