## 2 Lifting Scheme  
The lifting scheme was first proposed by [PERSON] and [PERSON], and then modified into flipping structure by [PERSON] et al. [18], shown as follows:  
\[1/\alpha\times y(2n+1)=1/\alpha\times x(2n+1)+x(2n)+x(2n+2) \tag{1}\]  
\[1/\beta\times y(2n)=1/\beta\times x(2n)+y(2n-1)+y(2n+1) \tag{2}\]  
\[1/\gamma\times H(2n+1)=1/\gamma\times y(2n+1)+y(2n)+y(2n+2) \tag{3}\]  
\[1/\delta\times L(2n)=1/\delta\times y(2n)+H(2n-1)+H(2n+1) \tag{4}\]  
\[H^{\circ}(2n+1)=K\times H(2n+1) \tag{5}\]  
\[L^{\circ}(2n)=1/K\times L(2n) \tag{6}\]  
where \(x\) represents the input pixel, \(y\), \(H\) and \(L\) mean temporal variables. \(H^{\circ}\) and \(L^{\circ}\) stand for the final results of high frequency and low frequency, respectively. \(\alpha\), \(\beta\), \(\gamma\), \(\delta\) and \(K\) are the constant coefficients. \(\alpha=-1.586134342\), \(\beta=-0.052980118\), \(\gamma=0.882911075\), \(\delta=0.443506852\), \(K=1.230174105\).  
The flipping structure can provide a variety of hardware implementations to improve and possibly minimize the critical path as well as the memory requirement of the lifting-based discrete wavelet transform [18]. Moreover, the flipping structure has less computational complexity and the forms of flipping formulas are highly consistent. From the observation of Equations (1)-(4), we can find that each equation involves a multiplication operation and two addition operations. And the four formulas are extremely similar with the same basic operational structure, which of (1) and (2) are shown in Figure 1. Thus, they can be considered as basic operations and can be reused to reduce the computing resources. For further analysis of the pipeline structure shown in Figure 1, considering that \(Tm\approx 2 Ta\)[14], the multiplication and addition operations in each basic operation can be performed simultaneously without any bad effect on the critical path, the multiplication items of the flipping method (2)-(4) arrive at least one clock cycle ahead of their respective addition items. For instance, if the multiplication item \(x(2n)\) in (2) arrives at the \(Xth\) clock cycle, the addition items \(y(2n+1)\) and \(y(2n-1)\) will be obtained through (1) at the \(Xth+1\) clock cycle at least, where \(X\) is defined as the number of clock cycles. So in each lifting scheme for (2)-(4), multiplication items will arrive one clock cycle advanced than the addition items as well.  
From Figure 1, it can be perceived that each basic operation module is completed within one clock cycle, so that the addition terms arrive just one clock cycle behind the multiplication term in the next formula. Thus, when the addition terms arrive in the current clock cycle, the two additions will be implemented with the multiplication item which has been multiplied. This method can not only minimize the number of registers, but also ensure the critical path of \(2 Ta\). Meanwhile, the multiplication factors can be selected to achieve the reuse of basic operation modules, since the four basic operations only differ in multiplication factors.  
Figure 1: Basic operation structures of (1) and (2). Note: The items with \({}^{*}\) are the multiplication terms that should arrive ahead of time.