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Singular value decomposition (SVD) of a matrix $\mathbf{A}$ is given by $\mathbf{A} = \mathbf{USV}^\top$ where $\mathbf{U}$ and $\mathbf{V}$ are orthogonal matrices and $\mathbf{S}$ is a diagonal matrix.

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Eigenvalue decomposition/SVD and the filtering perspective

SVD performs a decomposition based on the spatial structure of a matrix (image) whereas a spectral filters look at its frequency components. … The "equivalent" operation to lower the rank in SVD decomposition would be to apply a low pass filter in the frequency domain. …
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