The use of a nonlocal self-similarity (NSS) prior, which refers to each reference patch always having many nonlocal similar patches, has demonstrated its effectiveness in seismic data random noise attenuation because of the repetitiveness of textures and structures in their global position. However, NSS-based approaches face challenges when dealing with seismic interpolation. In the presence of missing traces, similar patch matching may be highly unreliable, resulting in a limited performance of interpolation. To solve this problem, a two-stage iterative seismic-interpolation framework based on a rank-reduction (RR) algorithm is developed. In the first stage, preinterpolation seismic data are used to guide the similar patch matching, and the problem of missing trace recovery for the stacked matched patches is converted to the problem of low-rank matrix completion. In the second stage, the similar patches are directly searched on the interpolation result after stage 1 without external help; that is, exploiting its own NSS, which can achieve enhanced interpolation performance. For each iteration, we obtain accurate similarly matched groups and apply a simple and efficient truncated singular value decomposition for RR. Owing to the unique construction method of a low-rank matrix formed by similar patches, our approach can handle irregularly or regularly sampled seismic data. Numerical experiments verify the effectiveness of our method, compared with the curvelet, low-rank matrix fitting, and f-x prediction filtering methods.

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