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We propose a local low-rank factorization approach to improve the efficiency and robustness of multidimensional deconvolution. The approach divides the sought-after Green’s function matrix into tiles, leveraging local rank characteristics to represent off-diagonal tiles as low-rank products and diagonal tiles as either low- or full-rank products, all controlled by user-specified accuracy requirements, trading off accuracy for storage and computational efficiency. The method is evaluated on a large-scale 3D synthetic example based on the EAGE/SEG Overthrust model, and results demonstrate significant improvements over benchmark solvers. In particular, as an extra benefit of rank-based filtering, the proposed method shows greater robustness to noise and sparse shot sampling, achieving higher signal-to-noise ratios and eliminating artifacts such as remnant multiples and near-offset noise. This work presents a promising solution for multidimensional deconvolution, particularly under challenging data conditions, and highlights the benefits of adaptive tile-based low-rank factorization for seismic data processing.