基于压缩感知的超分辨显微成像理论研究

Super-resolution microscopy imaging technologies such as STORM (stochastic optical reconstruction microscopy) have many shortcomings such as slow image acquisition and reconstruction, complex operation process, large amount of data, low spatial and temporal resolutions. These above shortcomings can be overcome if all fluorescent molecules were excited and imaged simultaneously. Compressed sensing can change the traditional pattern of acquisition and processing. However, super-resolution microscopy imaging based on compressive sensing is still in its infancy, and further theoretical research has not been carried out. This project would solve primarily the basic theory problem of super-resolution microscopy imaging based on compressive sensing through theoretical analysis, mathematical proof and experimental validation based on STORM. It lays the foundation for the practical application. This project intends to focus on the measurement matrix based on the point spread function (PSF) to carry out the theoretical and experimental research such as theory limit of super-resolution microscopic imaging, noise reduction and de-noising of post processing model, reconstruction algorithm based on unchanged number of photon, the scale of multiple adjacent fluorescent molecules regarded as point light source, and sparseness and super-resolution reconstruction of ultra high density fluorescent molecules. Fast and efficient super-resolution microscopy imaging based on ultra-high density fluorescent molecules would be implemented at last. This project not only provides a new theory and technology for super-resolution microscopy imaging, but also opens up new field for the research on compressed sensing. Therefore, the project, in addition to the great theoretical value, but also had a broad engineering application prospect and great economic value.

STORM等超分辨显微成像技术有图像采集重构慢、操作过程复杂、数据量大和空间时间分辨率低等缺点。如能实现对全部荧光分子的同时激发和一次成像就能克服上述缺点。压缩感知能改变传统的采集处理格局。但是基于压缩感知的超分辨显微成像还处于起步阶段，深入理论研究尚未展开。本项目拟基于STORM，通过理论分析、数学证明和实验验证初步解决基于压缩感知的超分辨显微成像的基础理论问题，为实际应用奠定基础。本项目将围绕基于点扩散函数测量矩阵，开展超分辨显微成像的理论极限、后处理模型的降噪去噪、基于光子数不变的重构算法、多个相邻荧光分子可视为点光源的尺度、超高密度荧光分子的稀疏化和超分辨重构的理论和实验研究。最终实现超高密度荧光分子的高速高效超分辨显微成像。本项目不仅为超分辨显微成像提供新的理论和技术，还为压缩感知研究开辟新的领域。因此，本项目不但具有极大的理论价值，也具有广阔的工程应用前景和巨大的经济价值。

STORM等超分辨显微成像技术有图像采集重构慢、操作过程复杂、数据量大和空间时间分辨率低等缺点。如能实现对全部荧光分子的同时激发和一次成像就能克服上述缺点。本项目基于STORM，通过理论分析、数学证明和实验验证初步解决了基于压缩感知的超分辨显微成像的基础理论问题，为实际应用奠定基础。围绕基于点扩散函数测量矩阵，研究构建了超分辨显微成像的理论极限模型、原始图像的降噪去噪模型、基于光子数不变的重构算法、多个相邻荧光分子可视为点光源的尺度模型、超高密度荧光分子的稀疏化和超分辨重构的模型。最终实现超高密度荧光分子的高速高效超分辨显微成像，原始图像采集帧数仅需20帧，时间分辨率在国内外首次真正达到亚秒级。取得的重要结果包括：理论分析并实验验证了超分辨显微成像的理论极限，发现当前重构定位能力远远低于理论极限，基于压缩感知的超分辨显微发展还存在极大的空间和潜力；提出并构建了基于压缩传感和高分辨率相机的超分辨率显微成像的广谱去噪（WSD）算法。WSD在国内外首次真正实现单张超分辨显微原始图像的有效去噪，去噪能力可达7dB。除WSD外，目前国内外尚无适用于超分辨显微原始图像的有效去噪算法。WSD已申请美国专利；通过插值和binning构建了基于光子数不变的重构算法；通过分析重构后的超分辨图像中荧光分子和真实荧光分子的对应关系构建了多个相邻荧光分子可视为点光源的尺度模型；构建起后处理的高维椭球理论模型，基于TV算法、过渡矩阵和0-1编码实现了超高密度荧光分子的稀疏化、超分辨重构和超快成像。本项目不仅为超分辨显微成像提供新的理论和技术，还为压缩感知研究开辟新的领域。因此，本项目不但具有极大的理论价值，也具有广阔的工程应用前景和巨大的经济价值。