# Improved wavefield reconstruction from randomized sampling via weighted one-norm minimization

 Title Improved wavefield reconstruction from randomized sampling via weighted one-norm minimization Publication Type Journal Article Year of Publication 2013 Authors Hassan Mansour, Felix J. Herrmann, Ozgur Yilmaz Journal Geophysics Volume 78 Number 5 Page V193-V206 Month 08 Keywords compressed sensing, randomized sampling, Trace interpolation, weighted one-norm minimization Abstract Missing-trace interpolation aims to recover the gaps caused by physical obstacles or deliberate subsampling to control acquisition costs in otherwise regularly sampled seismic wavefields. Although transform-domain sparsity promotion has proven to be an effective tool to solve this recovery problem, current recovery techniques do not fully utilize a priori information derived from the locations of the transform-domain coefficients, especially when curvelet domain sparsity is exploited. We use recovery by weighted one-norm minimization, which exploits correlations between the locations of significant curvelet coefficients of different partitions, e.g., shot records, common-offset gathers, or frequency slices of the acquired data. We use these correlations to define a sequence of 2D curvelet-based recovery problems that exploit 3D continuity exhibited by seismic wavefields without relying on the highly redundant 3D curvelet transform. To test the performance of our weighted algorithm, we compared recoveries from different data sorting and partitioning scenarios for a seismic line from the Gulf of Suez. These tests demonstrated that our method is superior to standard $\ell_1$ minimization in terms of antialiasing capability, reconstruction quality and computational memory requirements. URL https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2013/mansour2013GEOPiwr/mansour2013GEOPiwr.pdf DOI 10.1190/geo2012-0383.1 Citation Key mansour2013GEOPiwr