# Study of Image Classification Accuracy with Fourier Ptychography
## 3 Results  
The results of Fourier Ptychography are shown in Figure 8, Figure 9, Figure 10 for different datasets. Figure 8 shows the results using MNIST and Fashion-MNIST. Lower resolution image, FPM reconstructed image, and original image based on CIFAR and CalTech 101 are shown in Figure 9. Similarly, the lower resolution image, FPM reconstructed image, and original image based on the flowers and apple pathology  
Figure 8: (**A**) Lower resolution MNIST image; (**B**) FPM reconstructed MNIST image; (**C**) original MNIST image; (**D**) lower resolution Fashion MNIST image; (**E**) FPM reconstructed fashion MNIST image; (**F**) original Fashion MNIST image. Figure 10: (**A**) Lower resolution apple pathology image; (**B**) FPM-reconstructed apple pathology image; (**C**) original apple pathology image; (**D**) lower resolution flowers image; (**E**) FPM-reconstructed flowers image; (**F**) original flowers image. Figure 9: (**A**) Lower resolution CalTech 101 image, (**B**) FPM reconstructed CalTech 101 image (**C**) Original CalTech 101 image (**D**) Lower resolution Fashion CIFAR image (**E**) FPM reconstructed CIFAR image (**F**) original CIFAR image. datasets are shown in Figure 10. Consistently, all four datasets show their effectiveness in the generation of higher resolution images using FPM reconstruction. The results of PSNR and SSIM, and classification accuracy for CIFAR, CalTech101, MNIST, Fashion-MNIST, flowers, and apple pathology datasets are shown in Table 1, Table 2, Table 3.  
The \(p\)-values, an indicator of the efficacy of the multiple linear regression, are shown in Table 4. It is also clear that all the F-Test \(p\)-values are less than 0.05 showing that a significant linear relationship exists between these variables within the linear regression model. PSNR and SSIM increased with higher values of numerical aperture. For the purpose of illustrating the increased image classification accuracy due to the increase in PSNR and SSIM, the neural network activation map under different numerical apertures is presented. Figure 12 shows the Google inception convolution neural network activation map and the reconstructed images corresponding to each numerical aperture. The reconstructed image on the top of Figure 12 is the input of the Google inception neural network, and the activation map is the gradient of the features learned from the neural network. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & **Numerical** & **Reconstruction** & \multirow{2}{*}{**PSNR**} & **SSIM** & **Classification** \\  & **Aperture** & **Method** & & & **Accuracy** \\ \hline \multirow{6}{*}{Flowers} & \multicolumn{3}{c}{Ground Truth} & Inf & 1 & 83.15\% \\ \cline{2-6}  & 0.5 & \begin{tabular}{c} FPM \\ Lower Resolution \\ \end{tabular} & 19.26 & 0.80 & 81.25\% \\  & 0.42 & \begin{tabular}{c} FPM \\ Lower Resolution \\ \end{tabular} & 18.42 & 0.68 & 74.19\% \\ \cline{2-6}  & 0.2 & \begin{tabular}{c} FPM \\ Lower Resolution \\ \end{tabular} & 18.66 & 0.70 & 76.30\% \\  & 0.59 & \begin{tabular}{c} FPM \\ Lower Resolution \\ \end{tabular} & 17.35 & 0.59 & 72.14\% \\ \cline{2-6}  & 0.05 & \begin{tabular}{c} FPM \\ Lower Resolution \\ \end{tabular} & 16.02 & 0.41 & 70.28\% \\  & 0.47 & \begin{tabular}{c} FPM \\ Lower Resolution \\ \end{tabular} & 15.33 & 0.47 & 49.18\% \\ \hline \multirow{6}{*}{Apple Pathology} & \multicolumn{3}{c}{Ground Truth} & Inf & 1 & 99.56\% \\ \cline{2-6}  & 0.5 & \begin{tabular}{c} FPM \\ Lower Resolution \\ \end{tabular} & 15.44 & 0.62 & 98.12\% \\  & 0.66 & \begin{tabular}{c} FPM \\ Lower Resolution \\ \end{tabular} & 15.32 & 0.66 & 97.32\% \\ \cline{2-6}  & 0.2 & \begin{tabular}{c} FPM \\ Lower Resolution \\ \end{tabular} & 15.28 & 0.66 & 91.23\% \\  & 0.67 & \
\begin{tabular}{c} FPM \\ Lower Resolution \\ \end{tabular} & 6.71 & 0.0082 & 90.12\% \\  & 0.64 &
\begin{tabular}{c} FPM \\ Lower Resolution \\ \end{tabular} & 6.64 & 0.0003 & 82.35\% \\ \hline \hline \end{tabular}
\end{table}