Hi Gunjan,

are you interested how you could compare the results of both?

Although both techniques decompose a signal, the results differ. While the wavelet transform gives you temporally resolved information on the occurence of specific pattern (or frequencies), PCA does not (of course you can search for specific pattern in the most important principal components afterwards, but it does not directly output it).

Greetings, Sebastian

ICA tried to identify independent components (not just second order/uncorrelated, like PCA), and its is a way of extracting individual signals from a mixture (see cocktail party problem).

Wavelet decomposition is one way to decompose a signal based on special bases (or basis functions), which have certain mathematical properties. It works well for describing images because of the fact that image pixels are correlated at multiple scales with their neighbors (spatial).

Both wavelets and ICA can be used for image denoising.

Conference Paper Wavelet Denoising vs ICA denoising for functional optical imaging

E.g. the above paper shows empirically that ICA is better than wavelets for extreme noise conditions and non-linearities.

Hi Gunjan,

In the WT, the signal is decomposed based on its frequency content. In this way, we can reconstruct frequency-based components (e.g. with a given frequency band). To my knowloedge, ICA can separate mixed signals (not decompose) based on the higher order statistics (kurtosis and negentropy), so it uses a mathematical metric and the physical meaning will depend on the case study.

@Vikas Ramachandra @Sebastian Zaunseder @Bruno Honório. Thanks for the answers. As both the methods, perform decomposition of signals. Wavelet used predefined basis, however, can we say that ICA generates an basis and then use it to decompose the signal? I am just thinking of this hypothesis, and thinking on how can I compare them.

Hi Gunjan,

Could you, please, share a reference where ICA is used to signal descomposition?

Thanks

http://scikit-learn.org/stable/modules/decomposition.html#independent-component-analysis-ica

Gunjan,

As I mentioned and your reference states, ICA " separates a multivariate signal into additive subcomponents" . It does not act as the wavelet analysis in the sense that it decomposes a (single) signal (not restricted to be 1D) in its sub-band frequency components... the "decomposition" in these two scenarios is quite different although sharing "decomposition" as the semantic...

You can compare using the compression ratio. Refer Gonzalez and Woods

That's a nice question. I see ICA as a dimensionality reduction tool and Wavelet transform as a dimentinalty increase tool.