# Sparseness-constrained data continuation with frames: applications to missing traces and aliased signals in 2/3-D

 Title Sparseness-constrained data continuation with frames: applications to missing traces and aliased signals in {2/3-D} Publication Type Conference Year of Publication 2005 Authors Gilles Hennenfent, Felix J. Herrmann Conference Name SEG Technical Program Expanded Abstracts Volume 24 Page 2162-2165 Organization SEG Keywords Presentation, SEG, SLIM Abstract We present a robust iterative sparseness-constrained interpolation algorithm using 2-/3-D curvelet frames and Fourier-like transforms that exploits continuity along reflectors in seismic data. By choosing generic transforms, we circumvent the necessity to make parametric assumptions (e.g. through linear/parabolic Radon or demigration) regarding the shape of events in seismic data. Simulation and real data examples for data with moderately sized gaps demonstrate that our algorithm provides interpolated traces that accurately reproduce the wavelet shape as well as the AVO behavior. Our method also shows good results for de-aliasing judged by the behavior of the ($f-k$)-spectrum before and after regularization. {\copyright}2005 Society of Exploration Geophysicists URL https://www.slim.eos.ubc.ca/Publications/Public/Conferences/SEG/2005/Hennenfent05SEGscd/Hennenfent05SEGscd.pdf DOI 10.1190/1.2148142 Presentation https://www.slim.eos.ubc.ca/Publications/Public/Conferences/SEG/2005/Hen... Citation Key hennenfent2005SEGscd