Study On The Reconstruction Of Seismic Data Based On Compressive Sensing Theory

Seismic data is irregular due to the influence of the environment of the datagathering and pre-processing. It will have adverse effects on post seismic data. Thereconstruction method based on compressive sensing theory can effectivelyreconstruct seismic data to improve the resolution.In the traditional seismic data gathering, because of the limitation of the Nyquistsampling theorem, the gathering and storage of seismic data needs higherrequirements, which brings a great challenge for the development of seismicexploration. Compressive sensing theory which is developed in recent years hasbroken through the limit of Nyquist sampling theorem, It suggests that, if the pendingdata itself is sparse, or in a transform domain is sparse, then it is possible toreconstruct the full data which can meet the precision.In general, seismic data is not sparse, but we can find a sparse transformationmethod to make it sparse in the transform domain. Fourier transform can turn theseismic data from time-space domain to frequency-wavenumber domain, which is aeffective method of sparse representation and provides a prerequisite for thereconstruction method based on compressive sensing theory.The iterative threshold shrinkage algorithm is a common method to reconstructseismic data, but it has a slow convergence speed and reduces the efficiency ofoperation. This paper quotes an iterative linear expansion of thresholds for L1-basedimage restoration to deal with the problem of seismic data reconstruction undercompressive sensing theory. Instead of estimating the reconstructed data throughminimizing the objective function, the authors parameterize the problem as a linearcombination of few elementary thresholding functions, which can be solved bycalculating the linear weighting coefficients. It is to update the thresholding functionsduring the process of iteration. The advantage of this method is that the optimizationproblem only needs to be solved by calculating linear coefficients for each time. Withthe elementary thresholding functions satisfying certain constraints, a globalconvergence of the iterative algorithm is guaranteed. At the same time, according tothe two step iterative shrinkage algorithm which can speed up the convergence rate,this paper also presents the theory and algorithm of two step iterative linear expansionof thresholds,. Comparing with the iterative threshold shrinkage algorithm, it shows afaster convergence speed.The experimental and the actual processing results prove that it can not only dealwith the problem of seismic data reconstruction and has a better noise immunity, butalso has the advantages of remarkable convergence speed.