what is wave-let?
I have a short explanation for EE who know Fourier Theory and want to know Wavelet.
In Fourier, we know any signal is combined from infinite sum of sine and cosine at different amplitue and frequency.
In waveletm instead of sine and cosine, It is something call mother wavelet that have the wavelet properties. It means each signal can have it own basis wavelet function.
So, in theory.. you have a signal. search through its data and find the best mother wavelet. the keep the coefficients (compare to amplitue&harmonics of fourier)
That's why wavelet compression is better. (you choose the best function, fourier must be sine/cosine)