Denoising signals (in particular, 2D arrays, such as images) can be done by removing the high frequency components of the discrete Fourier transform (which is related to convolution with a Gaussian kernel) or by removing the smallest singular values. I was wondering if there is a known, specific mathematical connection between these two approaches.
I've seen a little discussion on the topic here and here, but I didn't really glean much specifically except the mention of circulant matrices.