Spatially irregularly sampled seismic data is unavoidable due to natural obstacles or acquisition designed for compressive sensing. Seismic reconstruction aims to regularize field data and map them from an irregular acquisition grid to regular-grid coordinates. We develop reconstructing high-dimensional arbitrary irregular-grid data with a fast multidimensional singular spectrum analysis (FMSSA) algorithm. The FMSSA filtering algorithm, replacing the traditional multidimensional singular spectrum analysis (MSSA) algorithm, acts as a projection operator to avoid explicitly constructing block Hankel matrices, accelerate the rank-reduction procedure, and reduce the memory load. Our method, the interpolated-FMSSA, can reconstruct data deployed on an irregular grid by introducing an interpolation operator adapted to connect irregular-grid observations and desired regular-grid data without losing accurate spatial coordinates information. In addition, two commonly used Fourier-based methods for irregular-grid data reconstruction, a modified projection onto convex sets algorithm and the fast iterative shrinkage-thresholding algorithm, are used for comparison. Synthetic and real data examples show significant improvement in computational efficiency compared to the traditional I-MSSA method and improvement in reconstruction accuracy compared with the Fourier-based methods for 3D and 5D irregular-grid data reconstruction.

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