The PSO is used to optimize the scaling factor for the watermarking process. The scheme achieves high PSNR values for the watermarked images. [PERSON] and [PERSON] [38] presented DWT-singular value decomposition (SVD)-based self-adaptive differential evolution-based watermarking scheme in which multiple scaling factors are optimized to embed imperceptible watermarks. [PERSON] and [PERSON] [39] has developed a robust and secure watermarking model by combining the regression tree and firefly algorithms to optimize scaling factors. [PERSON] [40] presented a watermarking scheme to balance imperceptibility and robustness by combing entropy and a distinct discrete firefly algorithm for optimization. Using the Bat optimization algorithm, [PERSON] and [PERSON] [41] presented a robust and optimized digital image watermarking scheme based on the stationary wavelet transform to correct the geometric attack. [PERSON] et al. [42] proposed a watermarking scheme to optimize multiple scaling factors using online sequential extreme learning machine. [PERSON] and [PERSON] [43] used the meta-heuristic optimization approach to develop an optimized watermarking scheme. [PERSON] et al. proposed a framework-based statistical and morphological model that is capable of effectively executing concurrent denoising and enhancement procedures. The aim of this study was to devise a maximum a posteriori (MAP) estimator for the coefficient that is free from any noise. The utilisation of a statistical model eliminates the need for the estimation of the noise level and enables the model to automatically adapt to the observed image data. The methodology was devised with the aim of preserving the genuineness of the image's delicate characteristics [44]. To obtain a more robust and secure watermarking scheme, the majority of the aforementioned studies have shifted from traditional watermarking to either heuristic-search-based or nature-inspired watermarking techniques. Although many decomposition-based watermarking schemes exist, their efficacy is inferior. PSO has been used in a variety of research and application domains in recent years. PSO has gained widespread attention in recent years due to its ease of implementation and rapid convergence to acceptable solutions. Although the PSO method has been used to solve search and optimization problems, it is susceptible to becoming trapped in local optima. Therefore, the proposed technique combines the lifting wavelet transform (LWT) and the Hessenberg decomposition and approaches for nature-inspired optimization for watermark embedding. Extensive tests show that our proposed method outperforms previous approaches. The suggested optimal watermarking scheme provides better robustness. The major contributions of the proposed scheme are as follows:  
* The utilisation of the two-level transform LWT was employed to achieve the robustness of watermarked ultrasound medical images. * The use of the Arnold transform enhances the security of watermarked images. * The Hessenberg decomposition is employed to attain a high level of imperceptibility in watermarked images. * The PSO technique was employed to determine the optimal value of the multi-valued scaling factor in the proposed watermarking methodology. The rest of the paper is organized as follows: Section 2 provides an overview of the techniques we use and provides context for the conversation that follows. Section 3 explains the suggested research approach for watermark embedding and extraction. Section 4 discusses the results. Section 5 concludes our work.