Fourier reconstruction with sparse inversion

The problem of seismic data reconstruction is posed as an inverse problem where the objective is to obtain the Fourier coefficients that synthesize the signal. Once the coefficients have been found, they are used to reconstruct the data on a uniformly spaced grid. A non-quadratic model weight function is included to stabilize the inversion and to provide the additional information required to interpolate through gaps. In the reconstruction of a non-uniformly sampled trace, an image and a marine 3D VSP shot-record, the method shows improved reconstruction in large gaps and is less sensitive to the spatial bandwidth used in the inversion compared to Fourier reconstruction without the non-quadratic model weight function.