# Empirical Mode Decomposition and Sparsity

In what sense does empirical mode decomposition (EMD) bring out the sparsity in a signal?

For instance, if I had a signal $f$ and I broke it down into $n$ intrinsic mode functions (IMF), what should I do to get a representation that has very few nonzero components?

Generally when speaking of sparsity, we say that a signal is sparse in some basis. Since IMFs do not have a fixed basis, in what sense can they be (if at all) sparse?

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EMD? Are you referring to the Hilbert-Huang Transform? – Mohammad Oct 11 '12 at 20:14
Yes, I'm sorry, I should have mentioned it before. – Jaidev Deshpande Oct 11 '12 at 20:17

Yes. By dictionary I mean an arbitrary collection of functions (called atoms'') that you can use as building blocks by taking their linear combination for creating other functions. – Atul Ingle Oct 12 '12 at 21:06
If there are correlations in the IMFs, their PCA should give you a set of orthogonal vectors which span the same space as the original IMFs. Also note that there is generally a difference between signals which are compressible (exhibiting an exponential decay of coefficient magnitude in a target basis) and those which are sparse (having only a few non-zero entries). Compressible signals can be approximated by sparse signals by retaining coefficients with the top $K$ magnitude. This would introduce a standard error term of $||f - f_K||$ into whatever you're doing. – Eric Oct 12 '12 at 21:26