We propose a data reconstruction based on a combination of migration Kirchhoff-style algorithm that migrates coefficients obtained by curvelet decomposition of seismic traces over time and a demigration scheme that generate data to the desire location. Curvelet data reconstruction involves four steps: Curvelet decomposition of the seismic data, thresholding of the resulting curvelet coefficients, multiscale Kirchhoff like migration, and demigration or data reconstruction from the multiscale images. <br><br>The migration procedure applied to each curvelet scale is the same as conventional Kirchhoff migration but operates on curvelet coefficients. Since only the curvelet coefficients are migrated, the cost of curvelet-based migration is reduced compared to that of conventional Kirchhoff migration. <br>


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