# Robust Image Embedded Watermarking Using DCT and Listless SPIHT
## 4 Simulation Results and Analysis
### Quality of the Watermarked Images  
Tables 1-3 shows the compression performance comparison on the watermarked images for Lena, Barbara, and Boat images, respectively, using SPIHT, LSK and the proposed algorithm. The PSNR and SSIM performance is quite satisfactory below a BR (bit rate) of 0.25 bits per pixel (bpp). The corresponding compression ratio (CR) can be found using the formula CR = 8/BR, (i.e., CR = 32:1). The TAF (in %) and NC values are also listed. It can be noted from the Tables 1-3 that the  
extracted watermark using all the three algorithms are not recognizable above a BR of 0.25 bpp. As we increase the bit rate, the quality of the watermark and watermarked images is also improved. It can be seen from the Tables 1-3 that the proposed scheme provides better watermark quality and better compressed image quality at lossless compression mode for Lena, Barbara and Boat images. In lossy compression mode, our proposed scheme is highly competitive (with respect to watermarked image and the quality of extracted watermark) with SPIHIT and LSK in most of the BR. A comparison of the extracted watermark quality is figured out in the Figures 4-6 for Lena, Mandrill, and Boat images. For the Lena image (Figure 4), the proposed scheme outperforms NC and TAF values compared to the work by [PERSON] et al. [25] at all compression ratios. Additionally, our scheme outperforms [PERSON] et al. [40] above 12:1 compression ratios. The similar improvements are also observed for Mandrill and Boat images in Figures 5 and 6, respectively. We have not shown the comparison of TAF and NC values for Mandrill and Boat images due to unavailability of experimental datum by [PERSON] et al. [40]. Figure 7 shows the PSNR vs. Compression ratio for Mandrill, Lena, and Boat images. It is observed that for Mandrill image, our scheme outperforms the scheme by [PERSON] et al. [25] in all CRs, i.e., the quality of the watermarked image is better using our scheme. However, a similar trend is not visualized in Lena and Boat images for all CRs. This is because our scheme provides better robustness and compression performance for texture images than smooth images. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Image** & **Bit Rate (bpp)** & **Algorithm** & **PSNR (dB)** & **SSIM** & **NC** & **TAF (\%)** \\ \hline \multirow{8}{*}{Lena} & \multirow{2}{*}{0.25} & SPIHIT [35] & 31.24 & 0.9075 & 0.1317 & 65.15 \\  & & LSK [38] & 30.93 & 0.8974 & 0.3032 & 52.75 \\  & & Proposed & **30.93** & 0.8982 & **0.3201** & **51.61** \\ \cline{2-7}  & \multirow{4}{*}{0.5} & SPIHIT & 31.10 & 0.9167 & 0.9848 & 1.71 \\  & & LSK & 31.31 & 0.9301 & 0.9828 & 2.04 \\  & & Proposed & **31.36** & 0.9292 & **0.9848** & 1.86 \\ \cline{2-7}  & \multirow{4}{*}{1.0} & SPIHIT & 33.87 & 0.9600 & 0.9801 & 1.84 \\  & & LSK & 34.02 & 0.9621 & 0.9797 & 1.91 \\  & & Proposed & **34.13** & **0.9617** & **0.9804** & 1.94 \\ \cline{2-7}  & \multirow{4}{*}{1.5} & SPIHIT & 34.35 & 0.9658 & 0.9227 & 6.14 \\  & & LSK & 34.76 & 0.9677 & 0.9180 & 6.52 \\  & & Proposed & **34.76** & 0.9676 & 0.9149 & 6.32 \\ \cline{2-7}  & \multirow{4}{*}{2.0} & SPIHIT & 34.83 & 0.9686 & 0.9298 & 5.56 \\  & & LSK & 34.76 & 0.9677 & 0.9180 & 6.52 \\  & & Proposed & **34.90** & **0.9693** & 0.9257 & **5.26** \\ \cline{2-7}  & \multirow{4}{*}{2.5} & SPIHIT & 35.41 & 0.9738 & 0.9510 & 4.00 \\  & & LSK & 35.33 & 0.9733 & 0.9517 & 4.08 \\  & & Proposed & **35.44** & **0.9740** & **0.9598** & 4.07 \\ \hline
3.0 & SPIHIT & 35.65 & 0.9724 & 0.9490 & 4.08 \\  & & LSK & 35.52 & 0.9744 & 0.9480 & 4.28 \\  & & Proposed & **35.65** & 0.9739 & **0.9558** & **3.27** \\ \hline Lossless & SPIHIT & 35.83 & 0.9762 & 0.9841 & 1.36 \\  & LSK & 35.68 & 0.9754 & 0.9747 & 2.24 \\  & Proposed & **36.00** & 0.9750 & 0.9831 & **1.36** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PSNR (Peak signal to noise ratio), structural similarity (SSIM), tamper assessment function (TAF), and Normalized Correlation (NC) performance on the Lena Image’; SPIHIT: set partitioning in hierarchical trees; LSK: Listless SPECK.