Here we have an example of wavelet analysis of a polygon mesh. On the left we have the original model. Performing a wavelet transform provides us with a low resolution version along with a set of wavelet coefficients. These coefficients encode the differences between the two versions. The transform is reversible, so we could add these differences back, and come up with the original model.
We can now recursively apply wavelet transform until we get a very simple version. Then we can, if we want, create different resolution models by taking the base mesh, and, for example, adding back the wavelets a level at a time, until we reach the desired resolution.