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Low-rank matrix approximation has applications in many fields, such as 2-D filter design and 3-D reconstruction from an image sequence. In this paper, one issue with low-rank matrix approximation is investigated: heteroscedastic noise. In most of previous research, the covariance matrix of the heteroscedastic noise is assumed to be positive definite. This requirement restricts the usefulness of results derived from such research. In this paper, we extend the Wiberg algorithm, which originally deals with the missing data problem with low-rank approximation, to the cases, where the heteroscedastic noise has a singular covariance matrix. Experiments show that the proposed Wiberg algorithm converges much faster than the bilinear approach, and consequently avoids many nonconvergent cases in the bilinear approach. Experiments also show that, to some extent, the Wiberg algorithm can tolerate outliers and is not sensitive to parameter variation.