On 2011-01-18, Brad Smith wrote:

I've only seen this kind of thing done on 2D signals (i.e. images), where it is much faster to use two 1D convolution passes (one in each dimension) than to use the much larger 2D kernel.

The general version of this, within discrete math, is called lattice basis reduction. The most well known algorigthm there is http://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%93Lov%C3%A1sz_lattice_basis_reduction_algorithm . Wavelet shrinkage and the many chase algorithms over over-complete bases are simply continuous time ghosts of this basic process.
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