# Study of Image Classification Accuracy with Fourier Ptychography
## 4 Conclusions  
In this study, we have investigated image classification accuracy with and without FPM reconstruction with six different image classifiers. We have also compared the image classification accuracy for the FPM reconstructed image versus the lower resolution images shown in Figure 8, Figure 9, Figure 10. It is clear that the lower resolution image has lower image visualization quality than the FPM-reconstructed image. Such a finding is further reinforced by the significant difference between the lower resolution and FPM reconstructed images in terms of image classification accuracy, especially for the lower NA conditions (e.g., 0.05 NA). For MINST, Fashion MNIST, Cifar, Caltech 101, and customized training datasets, when NA is lower, the lower resolution image classification accuracy becomes significantly lower than that of an FPM-reconstructed image. In contrast, when the image quality is higher with a higher NA condition (e.g., 0.5 NA), the image classification performance differs less significantly between with and without FPM reconstruction, which is possibly limited by classifier capabilities. Nevertheless, the use of FPM reconstruction to improve image classification accuracy is meaningful because the lower NA image without FPM reconstruction suffers from a lower accuracy of image classification. This observation is clear across all six different datasets with different image classifiers. The catastrophic outcome is further supported by the finding that for the Caltech-101 dataset, the accuracy of image classification corresponding to lower NA (0.05) and lower resolution conditions is 87% lower than the ground truth. For this situation, the use of FPM reconstruction is indeed helpful, which improves the image classification accuracy from 4.75% to 20%. Our results also suggest that the capabilities of different classifiers differ in terms of their capabilities to deal with lower \begin{table}
\begin{tabular}{c c c} \hline \hline
**Multiple Linear Regression** & \(p\)**-Value** &
\begin{tabular}{c} **Statistical** \\ **Significance (\(p\) < 0.05)** \\ \end{tabular} \\ \hline MNIST & 0.0046 & Yes \\ Fashion-MNIST & 3.02 \(\times\) 10\({}^{-5}\) & Yes \\ CIFAR & 0.02 & Yes \\ CalTech101 & 1.87 \(\times\) 10\({}^{-6}\) & Yes \\ Flowers & 0.0032 & Yes \\ Apple Pathology & 0.04 & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 4: F-Test \(p\)-values for multiple linear regression between image classification accuracy, PSNR, and SSIM for MNIST, Fashion-MNIST, CIFAR, CalTech 101, and the flowers and apple pathology datasets. Figure 12: Visualization of the apple pathology images and Google inception convolution neural network activation map (gradient) at the 141 st layer. In total, the Google inception convolution neural network had 144 layers. The 141 st layer is followed by the fully connected layer, the softmax layer, and the output layer. The green color corresponds to the vanished gradient. Fewer features in the activation map corresponds to the reduction in gradient. NA images. The differences could be caused by different neural network structures. For example, the Google Inception Network is found to have better capabilities to retain the image classification accuracy even for the lower NA images, which is likely caused by the Inception module within the network to handle the lower resolution images. We further built multiple linear regression between image classification value (dependent variable) and PSNR and SSIM (independent variables). Results show that there is a linear relationship between the dependent variable and independent variables (Figure 8). The related regression F-Test \(p\)-value is also smaller than 0.05, which indicates that such a linear relationship is strong. The linear relationship implies that it is feasible to predict the image classification accuracy based on the PSNR and SSIM values. The impact of noises on image classification performance has been documented in previous literature [23; 24].