# An Innovative Recompression Scheme for VQ Index Tables
## 4 Experimental Results  
To evaluate the performance of our proposed scheme, we compared it with the SOC algorithm and the state codebook algorithm. The experiments were conducted using MATLAB R2024a on a Windows \(11\) laptop equipped with a \(3.20\) GHz AMD Ryzen 7 CPU and \(16\) GB of RAM. As shown in Figure 11, we used six \(512\times 512\) size \(256\) gray standard images: Elaine, Lena, Pepper, Wine, Woodland, and Zelda. For our codebook, we trained these six images \(100\) times using the LBG algorithm [11], with each image block sized at \(4\times 4\) pixels. Figure 11: Standard images sized \(512\times 512\) pixels. (**a**) “Elaine”. (**b**) “Lena”. (**c**) “Pepper”. (**d**) “Wine”. (**e**) “Woodland”. (**f**) “Zelda”. In order to compare the compression rates of different schemes, we use the bit rate (i.e., bits per pixel) as a metric. Equation (3) to Equation (5), respectively, show the bit rate of different schemes. We suppose we have an image of size \(M\times N\), and the trained codebook size is \(N_{c}\). Equation (3) shows the bit rate of the SOC algorithm, where \(n\) represents the bit number of the search-order code; \(num_{SOC}\) is the number of SOC indices used, and \(num_{VQ}\) is the number of VQ indices used. Equation (4) shows the bit rate of the state codebook algorithm, where \(num_{SC}\) is the number of state codebook indices, \(i\) represents the search range of the state codebook or the number of bits of the small state codebook, and \(j\) represents the number of bits in each small state codebook for the codeword quantity. Equation (5) shows the bit rate of the side match algorithm, where \(num_{SM}\) is the number of side match indices, and \(r\) represents the number of bits in the matching range, usually set to \(r=4\). \[BR_{SOC}=\frac{num_{SOC}\times(1+n)+num_{VQ}(1+log_{2}N_{c})}{M\times N}, \tag{3}\]  
\[BR_{SC}=\frac{num_{SOC}\times(1+n)+num_{SC}\times(2+i+j)+num_{VQ}\times(2+log_{ 2}N_{c})}{M\times N}, \tag{4}\]  
\[BR_{SM}=\frac{num_{SOC}\times(1+n)+num_{SM}\times(2+r)+num_{VQ}\times(2+log_{ 2}N_{c})}{M\times N} \tag{5}\]  
For the sake of fairness in the experiment, we make comparisons in the cases of \(n=2\), \(n=3\), and the best \(n\), respectively. Here, n represents the number of bits for the SOC index, as the best \(n\) values vary for different methods. In addition to fixing \(n\) at 2 and 3 for comparison, the best \(n\) represents the value of n in the best-case scenario for the bit rate. Table 3 shows the comparison of bit rates and improvement rates using a codebook with 256 codewords. Please be aware that in the context of traditional VQ compression, when the codebook size is 256, the bit rate is 0.5. It can be seen from Table 3 that our method is significantly better than the SOC algorithm, with an average improvement rate as high as 13.41% in the case of \(n=2\). Additionally, the bit rate of our scheme is significantly lower than that of the state codebook algorithm. The main reason for this is that the side match algorithm relies on edge similarity. This approach can represent the details and differences between image blocks more accurately. This enables the algorithm to find more accurately matching indices.