## 3 Datasets and Evaluation Metrics
### MUSIQ  
The Multi-scale Image Quality Transformer evaluates image quality without reference using a Transformer-based architecture. The calculation involves dividing the image into patches at multiple scales, processing these patches through Transformer blocks with multiscale attention to capture local and global information, and then aggregating the resulting representations to predict a final quality score. Like other deep learning-based metrics, its complexity prevents a simplified mathematical representation of the calculation [107]. The higher the prediction value, the better the visual quality of the image. SSIM (Structural Similarity Index)  
The Structural Similarity Index (SSIM) [94] calculates the structural similarity between two images--considering luminance, contrast, and structure--providing a measure of how faithful the distorted image is compared to the reference [102]. The mathematical representation of the SSIM is given in Equation (2). \[SSIM(x,y)=\frac{(2\mu_{x}\mu_{y}+C_{1})(2\sigma_{xy}+C_{2})}{(\mu_{x}^{2}+\mu_ {y}^{2}+C_{1})(\sigma_{x}^{2}+\sigma_{y}^{2}+C_{2})} \tag{2}\]  
where \(\mu_{x}\) and \(\mu_{y}\) are the local means of images \(x\) and \(y\); \(\sigma_{x}^{2}\) and \(\sigma_{y}^{2}\) are the variances; \(\sigma_{xy}\) is the covariance; and \(C_{1}=(K_{1}L)^{2}\) and \(C_{2}=(K_{2}L)^{2}\) are constants to stabilize the division, with \(L\) being the maximum pixel intensity value (e.g., 255 for 8 bits). Values closer to 1 indicate better similarity. MS-SSIM (Multi-Scale SSIM)  
As an extension of the SSIM, the Multi-Scale SSIM (MS-SSIM) [94] evaluates local and global image characteristics at multiple scales, although it places less emphasis on brightness [103]. Its mathematical formulation is found in Equation (3). \[MS\text{-}SSIM(x,y)=[l_{M}(x,y)]^{\alpha_{M}}\prod_{j=1}^{M}[c_{j}(x,y)]^{\beta _{j}}[s_{j}(x,y)]^{\gamma_{j}} \tag{3}\]  
where \(l_{M}\) is the luminance similarity at scale \(M\); \(c_{j}\) and \(s_{j}\) are the contrast and structure comparisons at scale \(j\); and \(\alpha_{M}\), \(\beta_{j}\), and \(\gamma_{j}\) are weights assigned to each component. Values closer to 1 indicate greater structural similarity. FSIM (Feature Similarity Index)  
The Feature Similarity Index (FSIM) [104] considers phase congruency and gradient magnitude to assess image similarity, emphasizing edges and textures rather than pixel values. It can be determined by Equation (4). \[FSIM=\frac{\sum_{x\in\Omega}S_{L}(x)\cdot PC_{m}(x)}{\sum_{x\in\Omega}PC_{m}( x)} \tag{4}\]  
where \(S_{L}(x)\) is the local similarity based on the phase and gradient. \(PC_{m}(x)=\max(PC_{1}(x),PC_{2}(x))\) is the phase congruency map used as a weight; \(\Omega\) represents the set of all pixels. Values closer to 1 indicate greater perceptual similarity. VSI (Visual Saliency-Induced Index)  
The Visual Saliency-Induced Index (VSI) [105] incorporates saliency maps to assign greater weight to visually relevant regions, simulating how humans perceive visual quality. Equation (5) shows its mathematical representation:  
\[VSI=\frac{\sum_{x\in\Omega}S(x)\cdot VSm(x)}{\sum_{x\in\Omega}VSm(x)} \tag{5}\]where \(S(x)\) represents the combination of saliency, gradient, and chromaticity similarity; \(VSm(x)=\max(VS_{1}(x),VS_{2}(x))\) highlights salient regions. Values closer to 1 indicate images of higher perceived quality. MSE (Mean Squared Error)  
The Mean Squared Error (MSE) [29] calculates the average of the squared differences in intensity between the pixels of the original and distorted images, quantifying the overall error through Equation (6). \[MSE=\frac{1}{mn}\sum_{i=1}^{m}\sum_{j=1}^{n}[x(i,j)-y(i,j)]^{2} \tag{6}\]  
where \(x(i,j)\) and \(y(i,j)\) are the pixel values of the original and distorted images; \(m\times n\) is the image size. Lower MSE values indicate less error and, therefore, better quality.