Necessary conditions on the lifting scheme for existence of wavelets in L/sub 2/(R)

Over the years many different libraries of biorthogonal wavelets have been designed. In addition, the lifting scheme has been developed which unifies the design of biorthogonal wavelets using a simple approach. The lifting scheme allows the custom design of wavelets while maintaining the biorthogonal constraint on the filter bank. A drawback of the lifting scheme is that it does not guarantee that the wavelet associated with the iterated filter bank exists in L/sub 2/(R). In practice this raises the possibility that the filter bank may produce numerical artifacts. We present some necessary conditions on the lifting scheme for the resulting wavelets to exist in L/sub 2/(R). Using these conditions, we show how valid wavelet bases can be easily generated from randomly perturbed biorthogonal filter banks.