# Improving DFT-Based Image Watermarking Using Particle Swarm Optimization Algorithm
## 2 Background and Contributions
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Reference** & **Year** & **Description** \\ \hline
[18] & 2020 &
\begin{tabular}{c} Robust watermarking to copyright protection based on integer wavelet transform (IWT) and guided dynamic \\ particle swarm optimization (GDPSO). \\ \end{tabular} \\ \hline
[19] & 2020 &
\begin{tabular}{c} Robust blind image watermarking based on intertwining \\ logistic map, hybrid domain using discrete cosine transform \\ (DCT) domain, discrete wavelet transform (DWT) domain, \\ and singular value decomposition (SVD), in conjunction with \\ multidimensional PSO. \\ \end{tabular} \\ \hline
[20] & 2020 &
\begin{tabular}{c} Blind watermarking for color images based on extreme pixel \\ adjustment (EPA), multi-bit partly sign-altered mean \\ modulation (MP-SAM), mixed modulation (MM), quaternion \\ discrete Fourier transform (QDFT), and PSO. \\ \end{tabular} \\ \hline
[21] & 2021 &
\begin{tabular}{c} Image watermarking scheme based on DWT and SVD using \\ human visual system (HVS) and PSO. \\ \end{tabular} \\ \hline
[22] & 2019 &
\begin{tabular}{c} Digital watermarking algorithm with dual embedding in \\ DCT-DWT-SVD domains, using PSO. \\ \end{tabular} \\ \hline
[23] & 2019 &
\begin{tabular}{c} Image watermarking using normalized block processing \\ (NBP), normalized singular value decomposition (NSVD), \\ IWT, DCT, a genetic algorithm (GA) and PSO. \\ \end{tabular} \\ \hline
[24] & 2019 &
\begin{tabular}{c} Digital image watermarking based on SVD in complex \\ wavelet transform (CWT) domain, employing PSO and \\ Java algorithm. \\ \end{tabular} \\ \hline
[25] & 2019 &
\begin{tabular}{c} Robust image watermarking performed in multiple \\ transforms Lifting wavelet transform (LWT), DCT, discrete \\ fractional angular transform (DFAT), SVD, and PSO. \\ \end{tabular} \\ \hline
[26] & 2018 &
\begin{tabular}{c} Robust image watermarking based on hybrid domain \\ composed by LWT-DCT-SVD and using PSO. \\ \end{tabular} \\ \hline
[27] & 2018 &
\begin{tabular}{c} Digital image watermarking for industry applications in \\ DWT-SVD domain and employing GDPSO algorithm. \\ \end{tabular} \\ \hline
[28] & 2018 &
\begin{tabular}{c} Image watermarking with criteria of region of interest (ROI) \\ and region of non-interest (RONI), based on DWT-DCT-SVD \\ domain and using PSO algorithm. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: State of the art of invisible watermarking optimized by particle swarm optimization (PSO) algorithm. Figure 3: Aim of this proposal: find the optimized values of the key parameters in 2D DFT-based invisible watermarking. domains. In this way, motivated by this trend as well as by the promissory results in terms of imperceptibility and robustness obtained until now by the 2D DFT-based invisible watermarking; and justified by the necessity of improving aspects of information security related to ownership authentication and copyright protection, in this paper we propose a new improved 2D DFT-based invisible watermarking by the PSO algorithm, which is applied to color images. The main contributions of the proposed improved 2D DFT-based invisible watermarking by the PSO algorithm are:  
* Instead of using the metrics peak signal to noise ratio (PSNR)/structural similarity index (SSIM) in the fitness function of PSO algorithm, we employ the metric visual information fidelity (VIF) in conjunction with BCR criterion. It is known in the literature [29] that the VIF value reflects perceptual distortions more precisely than the PSNR.