Seismic Data Recovery with Curvelet Bivariate Shrinkage Function Based on Compressed Sensing

Recovery of under-sampled seismic data is a critical problem,in oil and gas exploration,therefore recovery algorithms with iterative shrinkage based on compressed sensing have been recently proposed. However most of these algorithms usually adopt a soft shrinkage function,which assumes that all of the sparse coefficients are independent of each other in curvelet or other domains,little attention has so far been devoted to the inter-dependencies of coefficients. In this paper,the dependencies of parent-child curvelet coefficients of seismic data are exploited by Bayesian estimation,moreover the new seismic data recovery algorithm via curvelet-based bivariate shrinkage function is proposed. First the respective parent-child curvelet coefficients joint distribution models of fully-sampled seismic data and noise signal caused by missing traces are established,then the bivariate shrinkage function according to the Bayesian maximum posterior probability estimation is obtained,finally the Landweber iterative shrinkage algorithm is used in the recovery process.When compared with existing recovery algorithms,it is proved that the proposed algorithm can obtain higher PSNR performance,and maintains the texture details better in events of seismic data

Recovery of under-sampled seismic data is a critical problem,in oil and gas exploration,therefore recovery algorithms with iterative shrinkage based on compressed sensing have been recently proposed. However most of these algorithms usually adopt a soft shrinkage function,which assumes that all of the sparse coefficients are independent of each other in curvelet or other domains,little attention has so far been devoted to the inter-dependencies of coefficients. In this paper,the dependencies of parent-child curvelet coefficients of seismic data are exploited by Bayesian estimation,moreover the new seismic data recovery algorithm via curvelet-based bivariate shrinkage function is proposed. First the respective parent-child curvelet coefficients joint distribution models of fully-sampled seismic data and noise signal caused by missing traces are established,then the bivariate shrinkage function according to the Bayesian maximum posterior probability estimation is obtained,finally the Landweber iterative shrinkage algorithm is used in the recovery process.When compared with existing recovery algorithms,it is proved that the proposed algorithm can obtain higher PSNR performance,and maintains the texture details better in events of seismic data recovery