Minimum weighted norm interpolation of seismic records

In seismic data processing, we often need to interpolate and extrapolate data at missing spatial locations. The reconstruction problem can be posed as an inverse problem where, from inadequate and incomplete data, we attempt to reconstruct the seismic wavefield at locations where measurements were not acquired. We propose a wavefield reconstruction scheme for spatially band-limited signals. The method entails solving an inverse problem where a wavenumber-domain regularization term is included. The regularization term constrains the solution to be spatially band-limited and imposes a prior spectral shape. The numerical algorithm is quite efficient since the method of conjugate gradients in conjunction with fast matrix-vector multiplications, implemented via the fast Fourier transform (FFT), is adopted. The algorithm can be used to perform multidimensional reconstruction in any spatial domain.