中文摘要：

目的高分辨傅里叶显微技术（FPM）是利用一组不同角度入射光下采集的低分辨率图像重建高分辨率图像的技术，该技术主要的理论基础是相位还原和综合孔径技术。低分辨图像和高分辨率图像在频域中的差异体现在高频段中的能量，高分辨率图像高频段能量更多。但是此前的方法重建的图像在高频段内的能量仍然较少。针对该问题，提出了一种新的FPM迭代更新模式——分频能量调整（BE）。方法基于高分辨率图像在傅里叶空间的能量分布的先验，在迭代过程中加入分频能量调整，来约束更新过程中的能量分布，从而使重建图像在能量上更接近于高分辨率图像，进一步提高图像的分辨率，突出边缘信息。结果在光学分辨率检验板和蚕豆气孔数据上对比增加光瞳函数恢复的FPM方法（EPRY—FPM）和添加分频能量调整的FPM方法（BE-FPM），实验表明，BE—FPM能进一步提高重建图像分辨率，突出边缘信息。为验证算法的鲁棒性，对样本添加模拟产生的高斯噪声和椒盐噪声，重建结果的视觉效果表明本文方法对噪声的鲁棒性更优。结论本文方法能进一步提高重建图像的分辨率，并且突出边缘信息。在噪声图像中比EPRY—FPM的更新模式具有更高的鲁棒性。在生物样本中，很多的图像具有相似的分布，而相似分布的样本在傅里叶空间的能量分布具有一致性，因此，BE—FPM方法在部分高分辨率样本重建大样本，单幅高分辨率样本重建同类样本等问题上有较大的应用潜力。

英文摘要：

Objective Fourierptychographic microscopy （FPM） is an imaging technique for reconstructing high-resolution images using low-resolution images acquired from a set of different angles of incident light. This technique can bypass the resolution limit of employed optics. The FPM algorithm comprises two main theoretical bases. The first one is the phase retrieval technique, which was originally developed for electron imaging. This technique is used to recover the lost phase information using intensity measurements, and it typically consists of alternating enforcement of the known information of the object in the spatial and Fourier domains. The second one is the aperture synthesis. This technique was originally developed for radio astronomy to pass the resolution limit of the single radio telescope. The basic idea of this technique is to combine images from a collection of telescopes in the Fourier domain to improve the resolution. By integrating the two techniques, the FPM can transform a conventional microscope into a high-resolution, wide field-of-view one. The difference between the low-resolution image and the high-resolution image in the frequency domain is reflected in the energy in the high-frequency band, and the high-frequency energy is abundant in the high-resolution image. However, the energy in the high-frequency band reconstructed by the former algorithm remains small. This study proposes a new iterative updating mode of FPM-band energy adjustment in FPM （BE-FPM） to solve the problem. Method This method is based on the energy distri- bution of Fourier space in high-resolution images. The entire iteration process for every image is divided into two steps. The first step conducts the recovery depending on the concepts of conventional FPM, which is to update the sub-region of the Fourier spectrum by the recorded low-resolution images. The second step is to use the new updating mode, namely, band energy adjustment in the iterative process. Energy distribution of a high-resolution image, which is calc