## 3 Proposed Technique
### Watermark Extraction Process
\begin{table}
\begin{tabular}{c c c} \hline \hline \(\alpha\) & **NC** & **SSIM** \\ \hline
0.001 & 1.0000 & 0.9891 \\
0.005 & 1.0000 & 0.9881 \\
0.010 & 0.9791 & 0.9001 \\
0.020 & 0.9715 & 0.8971 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Noise Attack with Different Intensity: NC and SSIM of Extracted Watermark. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\alpha\) &
\begin{tabular}{c} **Proposed** \\ **Work** \\ \end{tabular} & [28] & [31] & [30] & [32] \\ \hline
0.001 & 1.0000 & 0.9991 & 0.9893 & 0.9997 & 0.9988 \\
0.005 & 1.0000 & 0.9989 & 0.9901 & 0.9988 & 0.9981 \\
0.010 & 0.9791 & 0.9785 & 0.9888 & 0.9818 & 0.9881 \\
0.020 & 0.9715 & 0.9701 & 0.9725 & 0.9713 & 0.9711 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Noise Attack: Comparison of NC Values with Existing Schemes. Figure 9: Extracted Watermark after Noise Attack. The security of the embedded watermark is increased using the Arnold transform. ## 5 Conclusions

The power of PSO optimization in combination with the LWT and Hessenberg decomposition, a new blind image watermarking method, has been proposed. It is based on image segmentation and the Arnold cat map. A number of tests were performed on the system to determine its stability, and the findings are compared to those of other similar schemes. The suggested method generated watermarked images with PSNRs between 59.07 and 59.43 when compared to previous schemes. Despite significant distortions caused by JPEG compression, additive noise, median filtering, or average filtering, the watermark can still be extracted from the image. The removal of the watermark from a compressed watermark image results in an increase in perceived quality. The NC value of the retrieved watermark shows how good it looks. Based on the results of the experiments, our suggested method does a better job of reducing distortion than the best methods that are currently being used. The watermarking technique presented in this study yields superior image quality as measured by PSNR, SSIM, and NC metrics, thus rendering it a viable option for medical image applications. Methodology, L.K. ; Validation, K.U.S. ; Formal analysis, I.K. and A.K. ; Data curation, T.S. ; Writing--original draft, L.K. All authors have read and agreed to the published version of the manuscript. This research received no external funding. For this study not involving humans or animals. Not applicable. Medical images used in this study were taken from an open database available at ([[https://medpix.nlm.nih.gov](https://medpix.nlm.nih.gov)]([https://medpix.nlm.nih.gov](https://medpix.nlm.nih.gov)), accessed on 12 April 2023). The authors declare that there are no conflict of interest. The following abbreviations are used in this manuscript:

SVD Singular Value Decomposition

SLT Slantlet Transform

RSVD Randomized Singular Value Decomposition

FA Firefly Algorithm

MRI Magnetic Resonance Imaging

CT Computed Tomography

DICOM Digital Imaging and Communications in Medicine

JPEG Joint Photographic Experts Group

SSIM Structural Similarity Index Metric

PSNR Peak Signal-to-Noise Ratio

NC Normalized Correlation

NIA Nature Inspired Algorithm

MSF Multi-valued Scaling Factor

SSF Single-valued Scaling Factor

LWT Lifting Wavelet Transform

IWT Integer Wavelet Transform

PSO Particle Swarm Optimization \begin{table}
\begin{tabular}{c c c} \hline \hline \(\alpha\) & **NC** & **SSIM** \\ \hline
0.001 & 1.0000 & 0.9891 \\
0.005 & 1.0000 & 0.9881 \\
0.010 & 0.9791 & 0.9001 \\
0.020 & 0.9715 & 0.8971 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Histogram Equalization Attack: NC and SSIM of Extracted Watermark. ## References

* [1] [PERSON] _Digital Imaging and Communications in Medicine (DICOM): A Practical Introduction and Survival Guide_, 1 st ed. ; Springer Publishing Company, Incorporated: Berlin/Heidelberg, Germany, 2010. * [2] [PERSON]; [PERSON]; [PERSON]; [PERSON] Towards Touch-Based Medical Image Diagnosis Annotation.