Design of an algorithm for the reconstruction of 3-D seismic images from compressed data

This paper presents the implementation of an algorithm in Matlab to perform the reconstruction of a 3D seismogram from a small number of samples randomly acquired, using the compressed sampling technique. This technique is based on the concept that the signals to be sampled must be sparse in Wavelet or Curvelet domain. In order to do the reconstruction of the 3D seismic image, an interior point method that solves a least squares ℓ₁ regularized optimization problem is used. This algorithm is used to reconstruct the signal sparse coefficients. At the end of this paper there is a comparison among the reconstructed 3D seismogram with the original seismograms to verify the efficiency in this implementation, and the possible future application in the acquisition process of seismic traces.