On the arithmetic and bandwidth complexity of the lifting scheme

The lifting scheme (LS) is a very efficient implementation of the discrete wavelet transform (DWT). We compute the arithmetic gain realized when the LS is used instead of conventional filter banks. It is shown that, contrary to what was presented in the original work from W. Sweldens (see Appl. Comput. Harmon. Anal., vol.3, no.2, p.186-200, 1996), a gain of four is possible. However, the LS should be used with care as it can increase the memory bandwidth. Some implementations are presented together with their impact on the bandwidth. By using a common buffer for all filters, the bandwidth can be reduced to the case of the polyphase implementation. Using the method presented in this paper allows a memory bandwidth efficient implementation of the LS