Fourier叠层成像(FP)是一种新兴计算成像技术，可利用低数值孔径、低放大倍率物镜对微小样本实现大视场、高分辨率成像．针对目前该技术存在的瓶颈问题——成像质量对数据扰动敏感且重构过程计算复杂度高，本项目以设计和利用背景先验降低二次逆问题的病态程度为突破口，结合基于先验的正则化与深度神经网络方法缩减解空间维数，进而降低算法复杂度．通过研究：(1)FP问题解的唯一性和稳定性；(2)利用背景信息构建相位恢复模型与高分辨快速成像算法；(3)FP成像模拟与参数优化等内容，建立一种可用于FP快速成像的新型图像重构理论与方法．一方面发展基于背景先验的新型正则化理论与算法，为严重病态PR问题的数值解、间接测量数据的高精度重构等问题提供理论支撑；同时突破现有算法计算复杂度高、受噪声影响明显等难点，为基于FP的小目标高精度快速反演、快速病理检测和疾病诊断等应用提供技术支持．

Fourier ptychography (FP) is a newly proposed computational imaging technology which has the ability to give wide-field, high resolution image by low NA and low magnification objective lenses. But there are obstacles to its application. It is hard for FP to give real-time image. The reconstructed images are sensitive to various noise. Furthermore, some basic theoretical problems have not been studied intensively. In this project, we select the regularization method and deep neural network to decrease the dimension of solution space based on the background information, and then explore a new framework of stability and low cost phase retrieval method. The following closely related topics will be investigated carefully: (1) the uniqueness and stability of FP solution, (2) the new types of numerical algorithms for phase retrieval with low computational complexity based on background information, and (3) the optical simulations and optimization of the imaging systems. A new type of regularization method will be developed together with its theory, and a new approach for a series of problems will be supplied such as the restricted data reconstruction from indirect measurements. At the same time, the results of this project are in the hope of giving notable support for various phase-based applications including small object reconstruction and pathological diagnosis.