# Study of Image Classification Accuracy with Fourier Ptychography
## 1 Introduction  
Fourier Ptychography Microscopy (FPM) is a computational microscopy imaging technique potentially able to achieve a wide field of view and high-resolution imaging. It involves the use of a sequence of LEDs (LED array), which illuminates sequentially onto the target. Based on the sequential illumination, iterated sampling methods in the frequency domain are used for recovering higher resolution images [1, 2, 3]. Different types of Fourier Ptychography techniques have been proposed in the past for improving imaging resolutions [1, 2, 3, 4, 5, 6, 7]. Among them, multiplexed coded illumination techniques, laser-based implementations, aperture scanning Fourier Ptychography, camera scanning Fourier Ptychography, multi-camera approach, single-shot Fourier Ptychography, speckle illumination, X-ray Fourier Ptychography, and diffuser modulation have achieved successes [1]. More recent research has specifically addressed the Fourier Ptychography imaging problems such as the brightfield, phase, darkfield, reflective, multi-slice, and fluorescence imaging [3, 4, 5]. Driven by the significant interests in deep learning, a few different methods have been developed to solve the ill-posed Fourier Ptychography imaging problems. Notably, a convolutional neural network has been successfully applied for solving the Fourier Ptychography imaging problem [7]. The U-Net type structure-based generative adversarial network (GAN) was used to utilize fewer samples (26 images versus a few hundred images)for obtaining similar quality image reconstruction [8]. More promisingly, the U-Net plus GAN structure is proven able to reconstruct the high-resolution images using only a smaller amount of lower resolution image input data [9]. An interpretable deep learning approach has shown its effectiveness for the imaging of scattering materials [9; 10]. Until recently, the majority of Fourier Ptychography imaging studies have been primarily focusing on achieving high-resolution imaging based on the criteria of human visual perception satisfaction, yet a significant question left to answer is to understand the impact of such a technique on the broad spectrum of the downstream image processing related visual tasks such as classification, segmentation, and object detection. The ability to answer these questions is critical for applications such as industrial robotics, medical imaging, and industrial automation [10; 11]. It is well known that deep learning is time-consuming, thus imposing significant computational challenges. However, a significant research effort has been made where the recent breakthrough has shown that the training time of Imagenet has been reduced from days to hours, even further to minutes [12]. All these breakthroughs, however, come with a price. They all require expensive GPU devices for training the deep learning neural network. The expenses of the costly hardware can be well reflected through the price of the GPU card, for example, an NVIDIA P-100 GPU card costs about USD 6000 with the current market [12]. Training of all possible combinations of the different quality of FPM reconstructions for obtaining image classification accuracy is feasible but time-consuming and costly. As such, it is desirable to formulate the relationships between the FPM reconstructed image quality and the image classification accuracy in order to avoid training all the different combinations of the data and still able to identify the optimal parameters used for FPM reconstruction to achieve the best performance of the image classification accuracy [13; 14; 15; 16; 17; 18; 19; 20]. With this research, we propose to use the Fourier Ptychography technique to reconstruct higher (FPM-based) and lower resolution (without FPM) images for image classification. Following the FPM reconstruction, a deep convolution neural network is constructed for evaluation of the image recognition accuracy for both higher and lower resolution images.