Which filters do we use? You may settle for the Haar filter or
use more advanced filters, such as these
low-pass wavelet filters (the corresponding high-pass filters
can be construted using Kieffer 14, equation (8) and (14)).
Do we "wrap around" at the borders?
Which subbands do we choose to further decompose?
How do we quantize the resulting values and how do we encode them?
You may want to apply the framework from "lossless data compression".
Experiment with different choices and try to compress images or sound files. As always, measure rate and distortion. If you compress images, how do you compare with SPIHT?