## 4 Experiments and Analysis of Results
### Sample Quality Evaluation Indicator  
To evaluate the data generation capability of MDFT-GAN, this paper adopts a joint evaluation method based on sample quality metrics. This method includes Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), cosine similarity, and Pearson correlation coefficient, all of which are widely used in computer vision [34; 35; 36; 37]. These four metrics comprehensively assess pixel error, perceptual error, and feature distribution, providing a holistic evaluation of the quality of the generated images. The generative models used for comparison in this paper are GAN [18], ACGAN [28], DCGAN [38], WCGAN-GP [20], and the MDFT-GAN proposed in this paper.  
PSNR quantifies the overall pixel error between the generated image and the original image. The formula for PSNR is as follows:  
\[MSE=\frac{1}{MN}\sum_{i=1}^{M}\sum_{j=1}^{N}\bigl{(}x_{ij}-y_{ij}\bigr{)}^{2} \tag{21}\]  
\[PSNR=20\cdot\log_{10}\biggl{(}\frac{\mathrm{I}_{MAX}}{\sqrt{\mathrm{MSE}}}\biggr{)} \tag{22}\]  
where MSE denotes the mean square error; \(M\) and \(N\) denote the width and height of the image respectively; \(X_{ij}\) and \(Y_{ij}\) are the pixel values of the original and generated images, respectively; and \(I_{MAX}\) represents the maximum possible pixel value.  
SSIM evaluates the perceptual similarity between the generated image and the original image. Its formula is as follows:  
\[SSIM(x,y)=\frac{(2\mu_{x}\mu_{y}+C_{1})(2\sigma_{xy}+C_{2})}{(\mu_{x}^{2}+\mu_ {y}^{2}+C_{1})(\sigma_{x}^{2}+\sigma_{y}^{2}+C_{2})} \tag{23}\]  
where \(\mu_{x}\) and \(\mu_{y}\) are the means of the two images; \(\mu_{x}^{2}\) and \(\mu_{y}^{2}\) are their variances; \(\sigma_{xy}\) denote the covariance of the two images, respectively; \(C_{1}\) and \(C_{2}\) are constants to ensure computational stability.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Layer** & **Parameters** \\ \hline \multirow{8}{*}{Discriminator} & Input Data & \(3\times 64\times 64\) \\  & MDFT Block-1 & d = 1, emb = 64, n\_ heads = 8, in\_c = 3, \\  & out\_c = 64, k = 4\(\times\) 4, s = 2, p = 1 \\  & MDFT Block-2 & d = 1, emb = 128, n\_ heads = 8, in\_c = 64, \\  & out\_c = 128, k = 4\(\times\) 4, s = 2, p = 1 \\  & MDFT Block-3 & d = 1, emb = 256, n\_ heads = 8, in\_c = 128, \\  & out\_c = 256, k = 4\(\times\) 4, s = 2, p = 1 \\  & MDFT Block-4 & d = 1, emb = 512, n\_ heads = 8, in\_c = 256, \\  & out\_c = 512, k = 4\(\times\) 4, s = 2, p = 1 \\  & FC-1 & Out = Real/Fake \\  & FC-2 & Out = n\_classes \\ \hline \multirow{8}{*}{Classification} & Input Data & \(3\times 64\times 64\) \\  & Resblock-1 & in\_c = 3, out\_c = 64, s = 2, BN, ReLU \\  & Resblock-2 & in\_c = 64, out\_c = 128, s = 2, BN, ReLU \\  & Resblock-3 & in\_c = 128, out\_c = 256, s = 2, BN, ReLU \\  & ViT Encoder & emb = 768, patch = 16 \(\times\) 16, d = 12, n\_heads = 12 \\  & FC-1 & in = 768, Out = 512, ReLU, Dropout = 0.5 \\  & FC-2 & in = 512, Out = n\_classes \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._Cosine similarity (CS) measures the angular similarity between the original and generated images and is calculated as:  
\[CS(x,y)=\frac{x\cdot y}{\|x\|\|y\|} \tag{24}\]  
where \(x\) and \(y\) represent the vectorized forms of the two images.  
Pearson correlation (PC) coefficient assesses the linear correlation between the original and generated images. It is defined as:  
\[PC(x,y)=\frac{\sum_{i=1}^{N}(x_{i}-\overline{x})(y_{i}-\overline{y})}{\sqrt{ \sum_{i=1}^{N}(x_{i}-\overline{x})^{2}}\sqrt{\sum_{i=1}^{N}(y_{i}-\overline{y} )^{2}}} \tag{25}\]  
where \(x_{i}\) and \(y_{i}\) are the \(i\)th pixel values of the two images; \(\overline{x}\) and \(\overline{y}\) are their mean pixel values; and \(N\) is the total number of pixels.