# Fourier Ptychographic Reconstruction Method of Self-Training Physical Model
## 1 Introduction  
The microscope is an optical instrument consisting of single or multiple lenses. It is an important part of the production, life, and research fields such as clinical medicine and industrial inspection. In 2013, [PERSON] 'an et al. proposed a new imaging technique called Fourier ptychographic microscopy (FPM) [1]. FPM is a computational imaging technology with a large field of view and high resolution. Fourier ptychographic microscopy combines synthetic aperture [2; 3; 4; 5; 6; 7; 8; 9; 10; 11], phase retrieval [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23], optimization theory [24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36], and other concepts to break many limitations of traditional microscopes. Different from the traditional microscope, Fourier ptychographic imaging is a series of low-resolution intensity images collected by Fourier ptychographic microscopy system. Combined with a reconstruction algorithm, high-resolution intensity and phase images are reconstructed from the collected low-resolution images. The imaging process is as follows: the samples are illuminated successively with different LED incident angles, a set of low-resolution (LR) images with different spatial spectra are captured accordingly, and then these spectral sub-apertures obtained from the low-resolution images are spliced together in the Fourier domain to reconstruct the entire high-resolution (HR) spatial spectrum. In short, onlythe low-resolution intensity image corresponding to the high-resolution spatial spectrum sub-aperture image is obtained, and the low-resolution intensity image is used to restore the high-resolution spatial spectrum. The traditional G-S (Gerchberg-Saxton) method [37] generates phase information by changing the phase gradient caused by oblique incident illumination, thereby achieving synthetic aperture and reconstructing high-resolution complex amplitude images. The iterative update process of this reconstruction method uses the traditional gradient descent method to obtain the global optimal solution. Since FPM technology was proposed in 2013, researchers have proposed many improvements to FPM reconstruction algorithms, such as Gauss-Newton [38], Wirtinger flow [39] (Wirtinger flow optimization), adaptive step [40] (A-S, adaptive step-size), and other optimization algorithms. However, the traditional reconstruction algorithm of Fourier ptychographic microscopy requires more iterative updates, which cannot escape the idea of gradient descent, and the reconstruction effect is poor. Researchers have focused their research on neural networks and deep learning. By using neural network algorithms, the computing power of computational imaging can be improved. For example, the neural network modeling method proposed by [PERSON] et al. [41] uses back propagation as a tool to solve the global optimal solution; the deep learning method [42; 43; 44; 45] has the advantages of high processing performance and fast operation speed. It can be used in Fourier laminated microscopic computational imaging technology to solve the problem of image reconstruction quality. The author proposed an FPM reconstruction algorithm based on the SwinIR physical model [46] at the 2022 ICAITA International Conference. The algorithm completes the reconstruction by screening the appropriate network parameters and using the trained weights. At the same time, fast and high-quality target image reconstruction is realized. The results show that it has strong robustness to noise, fast reconstruction speed, and high reconstruction quality. At present, deep learning and machine learning have developed rapidly, and have been studied in many aspects such as machine crown segmentation [47], music [48], life prediction [49], and image classification [50].