## 2 Related Work  
As already mentioned, FR-IQA algorithms predict the perceptual quality of distorted images with full access to the reference images. The traditional and probably the simplest methods for FR-IQA are mean squared error (MSE) and peak signal-to-noise ratio (PSNR), which rely on the measurement of the distortion energy of the images. However, their performance lags behind other more sophisticated metrics, since their results are not consistent with human quality perception [22]. Hence, many FR-IQA methods have tried to build on the properties of the human visual system (HVS) to compile effective algorithms. For example, the structural similarity index (SSIM) [23] utilizes the observation that HVS is sensitive to contrast and structural distortions. More specifically, SSIM [23] applies local sliding windows on the reference and distorted images and measures luminance, contrast, and structure similarity using predefined functions containing average, variance, and covariance computations. Finally, the perceptual quality of the distorted image is obtained by taking the arithmetic mean of the similarity values of the local sliding windows. [PERSON] et al. [24] investigated the mathematical properties of SSIM and pointed out that SSIM satisfies the identity of indiscernibles and exhibits symmetry properties, excluding the triangle inequality. SSIM has become quickly popular in the signal processing community and gained a significant amount of attention for further research [25]. For example, [PERSON] et al. [26] extended SSIM into MS-SSIM by conducting multi-scale processing. Further, [PERSON] et al. [27] utilized complex wavelet domains to define a new structural similarity index. In contrast, [PERSON] et al. [28] modified SSIM to compare edge information between the reference and the distorted images. In addition to structural degradation, image gradient is also a popular feature in FR-IQA. Specifically, [PERSON] et al. [29] defined an FR-IQA metric using gradient similarity between the reference and distorted images. Similarly, [PERSON] and [PERSON] [30] utilized gradient similarity, but scale information was also incorporated into their metric.  
Motivated by the success of deep learning in many image processing tasks [31; 32; 33], deep learning has also appeared in FR-IQA. For example, significant amount of proposed works compare deep activations of convolutional neural networks (CNNs) for a reference-distorted image pair to establish an FR quality metric. For example, [PERSON] et al. [34] extracted feature maps using an AlexNet [35] CNN. Subsequently, the extracted feature maps were compared using histogram intersection kernels [36] and a similarity value was produced for each feature map. To obtain perceptual quality, the arithmetic mean of these similarity values was taken. Later, this approach was developed further [37] by replacing the histogram intersection kernels by traditional image similarity metrics. Another line of work focused on training end-to-end deep architectures on large IQA benchmark databases [38; 39; 40]. [PERSON] et al. [39] investigated vision transformers and self-attention for FR-IQA. Namely, a context-aware sampling procedure was introduced to extract patches from the reference and the distorted images. Next, the patches were encoded by a vision transformer.  
Another class of FR-IQA methods uses existing and available FR-IQA metrics to construct a new metric with improved performance. For instance, [PERSON] [41] studied the characteristics of three different metrics. In addition, the authors introduced a combined metric by taking the exponentiated product of the examined three metrics. In contrast, other proposals utilized optimization techniques to find optimal weights for a linear combination of already existing FR-IQA techniques [42; 43; 44]. Instead of optimization, [PERSON] et al. [45]trained a neural network from scratch using traditional FR-IQA metrics as image features to obtain improved estimation performance.