Cascading the two channel filter banks produces arbitrary filter banks. Since the two-channel filter bank implements an orthonormal signal expansion, the cascaded filter bank also implements an orthonormal expansion. The filter bank may be used to construct an expansion adaptively to the signal characteristics. However, in practice it is difficult to determine the best filter bank structure without first expanding the signal. One solution is to over-expand the signal using a full cascade, and then choose the paths that gives the best complete expansion.
Images are inherently non-stationary signals.
The wavelet packet algorithm adapts to the whole image and not to different regions as needed. Therefore, we extend the wavelet packet algorithm by including the next building block of the joint image expansion - segmentation.