Construction of Biorthogonal Multiwavelets Using the Lifting Scheme

The lifting scheme has been found to be a flexible method for constructing scalar wavelets with desirable properties. Here it is extended to the construction of multiwavelets. It is shown that any set of compactly supported biorthogonal multiwavelets can be obtained from the Lazy matrix filters with a finite number of lifting steps. As an illustration of the general theory, compactly supported biorthogonal multiwavelets with optimum time–frequency resolution are constructed. In addition, experimental results of applying these multiwavelets to image compression are presented.