目的 高分辨傅里叶显微技术（Fourier Ptychographic Microscopy，简称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，本文提出了一种新的FPM迭代更新模式——分频能量调整（Band Energy Adjustment，简称BE）。方法 该方法是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（Embedded pupil function recovery for Fourier Ptychographic Microscopy，简称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明显地表明本文的方法对噪声的鲁棒性更优。结论 本文提出了一种新的FPM迭代更新模式，即分频能量调整。实验表明该模式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。
Application of band energy adjustment in Fourier ptychographic microscopy
KUANG Yawei,DUAN Chaijie(1.Graduate School at Shenzhen, Tsinghua University; 2. Department of Biomedical Engineering, Tsinghua University, Beijing.)
Abstract ： Objective Fourier ptychographic 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. It can bypass the resolution limit of employed optics. There are two main theory basis of FPM algorithm. The first one is phase retrieval technique, originally developed for electron imaging. It is used to recover the lost phase information using intensity measurements. It typically consists of alternating enforcement of the known information of the object in the spatial and Fourier domains. The second technique employed is the aperture synthesis. This technique was originally developed for radio astronomy, aiming at passing 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, FPM can transform a conventional microscope into a high-resolution, wide filed-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 more in the high resolution image. However, the energy in the high frequency band reconstructed by former algorithm is still small. To solve this problem, this paper proposes a new iterative updating mode of FPM - Band Energy adjustment in Fourier ptychographic microscopy (BE-FPM). Methods This method is based on the energy distribution of Fourier space in high-resolution images. The whole 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 Fourier spectrum by the recorded low-resolution images. The second step is to use the new updating mode--band energy adjustment in the iterative process. Energy distribution of a high-resolution image which is calculated from a similar high-resolution sample is applied as the prior. We divide the Fourier spectrum into several bands. Every band has different range of frequency. Then the energy of every band is calculated, and adjusted by the high-resolution prior. By adjusting the energy of different frequency bands, the reconstructed image is more close to the high-resolution image. So far, the iterative process for one image ends, then conducts the process for every captured low-resolution image with several times, until getting the convergence. The experiment results on resolution board and bean hole data demonstrate that the BE-FPM would further improve the resolution of the reconstructed image, and can highlight the edge information. Results We conduct the experiments on resolution board and bean hole data. Compared with the updating mode used in embedded pupil function recovery for FPM (EPRY-FPM) and the BE-FPM updating mode, we find that the BE-FPM mode can further improve the resolution of reconstructed image and highlight the edge information. The element of group eight in the resolution board has a better and clearer reconstruction effect in BE-FPM reconstruction result. Also, the boundary of bean hole achieves a much clearer reconstruction by using BE-FPM. What’s more, in order to prove the robustness of BE-FPM, Gaussian noise and the salt and pepper noise are added in the originally captured low-resolution images. By reconstructing the noisy images using EPRY-FPM and BE-FPM respectively, we proved that the robustness of BE-FPM for noise is better than EPRY-FPM. Conclusion This paper presents a new iterative updating mode of FPM, namely BE-FPM. Experiments on resolution board and bean hole data show that BE-FPM updating mode can further improve the resolution of the reconstructed image, and highlight the edge information. What’s more, BE-FPM updating mode is more robust than EPRY-FPM when the recorded images contains noise. In biological samples, a lot of images have similar distribution, and these samples also has similar energy distribution in the Fourier space. Therefore, BE-FPM would have potentials in reconstructing a whole sample using just partial high resolution image and reconstructing samples in the same class via a single high resolution image.