Parabolic dictionary learning searches for basis vectors that describe the elementary parabolic events in the seismic data. The set of parabolic basis vectors is called a parabolic dictionary. It defines a mathematical domain in which each coefficient corresponds to a parabolic event in the time-space domain. Then, the seismic data are interpolated or regularized using a sparse representation of the data in the parabolic dictionary domain. This interpolation method differs from conventional seismic data reconstruction methods in two respects: The transform domain is not predefined but data-driven, and the basis vectors do not exhibit linear structures but parabolic structures. The first characteristic strengthens robustness to noise and to aliasing, whereas the latter increases the interpolation quality when the sampling is too coarse to approximate the wavefield between neighboring traces by linear events. The parabolic dictionary learning method is tested for interpolation of the seismic data between the cables of a 3D towed marine survey and is shown to be superior to the anti-alias anti-leakage Fourier transform method.


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