Linear prediction filters in the domain are widely used to interpolate regularly sampled data. We study the problem of reconstructing irregularly missing data on a regular grid using linear prediction filters. We propose a two-stage algorithm. First, we reconstruct the unaliased part of the data spectrum using a Fourier method (minimum-weighted norm interpolation). Then, prediction filters for all the frequencies are extracted from the reconstructed low frequencies. The latter is implemented via a multistep autoregressive (MSAR) algorithm. Finally, these prediction filters are used to reconstruct the complete data in the domain. The applicability of the proposed method is examined using synthetic and field data examples.