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The design of two-dimensional (2-D) digital filters can be accomplished using the singular-value decomposition (SVD) method proposed by the authors in the past. The method in its present form treats all the elements of the sampled frequency-response matrix uniformly. Although the method works very well, in certain applications improved designs can be achieved by preconditioning the frequency-response matrix in order to emphasize important parts and deemphasize unimportant parts of the matrix. The preconditioning can be achieved through the use of an optimal weighted low-rank approximation (WLRA). Current methods for WLRA provide only local solutions. In this paper, we propose a method that can be used to perform WLRA which is globally optimal for complex-valued matrices. The usefulness of the proposed method is demonstrated by applying it to the design of 2-D digital filters.