# 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 Submitted Year of Publication 2012 Authors Hassan Mansour, Felix J. Herrmann, Ozgur Yilmaz Month 10 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. While transform-domain sparsity promotion has proven to be an effective tool to solve this recovery problem, current recovery techniques make no use of a priori information on the locations of transform-domain coefficients. In this paper, we propose recovery by weighted one-norm minimization, which exploits correlations between the locations of significant 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 illustrate the performance of our weighted algorithm, we compare recoveries from different scenarios of partitioning for a seismic line from the Gulf of Suez. These examples demonstrate that our method is superior to standard $\ell_1$ minimization in terms of reconstruction quality and computational memory requirements. URL https://www.slim.eos.ubc.ca/Publications/Private/Submitted/Journal/mansour2012iwr/mansour2012iwr.pdf Citation Key mansour12iwr