# Study of Image Classification Accuracy with Fourier Ptychography
## 4 Conclusions
Specifically, Figure 12 shows the activation maps, which are the gradient features learned from the Google inception neural network. It is evident that for the low numerical aperture, which is associated with a lower SSIM and PSNR, more learned gradient features become vanished or reduced. The vanished gradient compromises the network classification accuracy. It is clear that a more vanished gradient in the learned features corresponds to the lower numerical apertures of 0.1 and 0.3, thus compromising network classification accuracy. For a 0.5 numerical aperture, the vanished gradient has been reduced, which, therefore, corresponds to the improved image classification accuracy. This study had some limitations. First, a greater number of trials for training and the evaluation of image classification accuracy for different NAs are needed. The linear relationship between SSIM, PSNR, and image classification accuracy needs to be evaluated based on a greater number of such trials. Specifically, under extreme lower or higher NA conditions, e.g., lower than 0.05 NA or greater than 0.5 NA, an examination of the relationship is also needed. Furthermore, factors involved in the study are limited. We have not included different noises, training and testing data ratios, or a more extensive number of classifiers. We plan to address the limitations in future work. Conceptualization, H.Z., Y.Z., L.W., Z.H., T.-C.P. and P.W.M.T. ; methodology, H.Z., W.Z., D.C. and L.W. ; software, H.Z. and D.C.; validation, Y.Z., T.-C.P. and P.W.M.T. ; formal analysis, H.Z. and T.-C.P. ; investigation, T.-C.P. ; resources, Y.Z. ; data curation, H.Z. ; writing--original draft preparation, H.Z. and L.W. ; writing--review and editing; T.-C.P., W.Z. ; visualization, Y.Z. ; supervision, T.-C.P. ; project administration, H.Z. and Y.Z. ; funding acquisition, Y.Z., P.W.M.T. All authors have read and agreed to the published version of the manuscript. National Natural Science Foundation of China (11762009, 61865007); Natural Science Foundation of Yunnan Province (2018 FB101); the Key Program of Science and Technology of Yunnan Province (2019 FA025); General Research Fund (GRF) of Hong Kong SAR, China (Grant No: 11200319). Not Applicable. The data used in this study include MINST, Fashion MNIST, Cifar, Caltech 101. They are available at the following URLs: MINST: [[http://yann.lecun.com/exdb/mnist/](http://yann.lecun.com/exdb/mnist/)]([http://yann.lecun.com/exdb/mnist/](http://yann.lecun.com/exdb/mnist/)); Fashion MNIST: [[https://www.kaggle.com/zalando-research/fashionmnist](https://www.kaggle.com/zalando-research/fashionmnist)]([https://www.kaggle.com/zalando-research/fashionmnist](https://www.kaggle.com/zalando-research/fashionmnist)); Cifar: [[https://www.cs.toronto.edu/~kriz/cifar.html](https://www.cs.toronto.edu/~kriz/cifar.html)]([https://www.cs.toronto.edu/~kriz/cifar.html](https://www.cs.toronto.edu/~kriz/cifar.html)); Caltech 101: [[http://www.vision.caltech.edu/Image_Datasets/Caltech101/](http://www.vision.caltech.edu/Image_Datasets/Caltech101/)]([http://www.vision.caltech.edu/Image_Datasets/Caltech101/](http://www.vision.caltech.edu/Image_Datasets/Caltech101/)). The authors declare no conflict of interest.