A folded multiplierless, lifting based wavelet pipeline

The lifting scheme (LS) based wavelet transform [1] is the decorrelation stage employed in JPEG2000 [2], where the 9/7 and the 5/3 wavelet filters are used for lossy and lossless compression respectively. It is known that the 5/3 wavelet filters can be implemented with a simple multiplierless two steps LS, whereas the 9/7 wavelet filters require non rational multiplications with four lifting steps and a scaling factor ζ. In Fig. 1 (a) the standard LS for the 9/7 wavelet filters is shown where the four lifting coefficients α, β, γ, δ and the scaling factor ζ are evidenced. Besides in Table I the first column summarizes the 9/7 lifting coefficients values whereas in the third column the 5/3 lifting coefficients values are given. As a consequence multipliers are required to calculate the 9/7 wavelet transform. Moreover, since the number of lifting steps is different for the 9/7 and the 5/3 wavelet filters, the number of clock cycles required to produce the results is different. In [3] the rational 9/7 lifting factorization proposed in [4] is combined with the flipping structure [5] to achieve a multiplierless architecture (see Fig. 1 (b) and Table I second column). The main drawback of the multiplierless lifting-flipping (LF) architecture described in [3] is the scaling factor (ζ = 4/5 in the normalized form) that ought to be embedded into the successive stage (e.g. the quantizer). In order to embody the 5/3 computation into the LF architecture some bypass multiplexers are required, leading to a 100% hardware use for the 9/7 computation and to near 50% hardware use for the 5/3. In this paper we show that the two lifting steps wavelet derived in [6] achieves near JPEG2000 9/7 performance with a significant complexity reduction. Moreover a multiplierless pipeline that embodies both the 9/7 and the 5/3 wavelet transform with 100% hardware utilization is shown.