What are the practical differences between SVD and wavelet transforms in data analysis?

The main difference between the two is that wavelet transforms use a wavelet basis while SVD uses an eigenfunction basis like the Fourier basis. They both offer the same functionality i.e. approximation of signals, and hence appear to resemble each other. But their overall properties are different. 

A wavelet basis is desirable, when the signal you are trying to decompose hashighly localized features or spatial variability such as edges in images or point singularities in a time series. It is well known that linear approximations are sub-optimal for representing signals that aren't smooth, i.e. don't lie in ellipsoids. AsLaurent Duval pointed out, wavelets form a non-linear approximation of a signal and are hence outperform linear approximations for such signals. The wavelet-vagueluette decomposition is an SVD like decomposition thats uses the wavelet basis and offers better approximation of the signal given localized features. [1] offers a better introduction to the usefulness of wavelets and wavelet-vaguelette decompositions as well as additional references.

[1] Wavelets and W.V.D 10 minute tour http://www.stanford.edu/~slansel...

from: http://www.quora.com/What-are-the-practical-differences-between-SVD-and-wavelet-transforms-in-data-analysis