基于多测量矢量压缩感知的超分辨荧光显微成像研究

在超分辨荧光显微成像技术中，单分子定位显微方法是被广泛应用的技术之一。根据荧光显微成像原理构造多测量矢量压缩感知模型（Multiple Measurement Vector-Compressed Sensing, MMV-CS），并采用多重稀疏贝叶斯学习算法进行求解，来实现超分辨荧光图像重建。分析了有效像元大小、荧光分子生成的光子数和背景信号泊松化噪声对重建结果的影响，以及在图像进行分块处理时算法运行时间的分析。模拟和实验计算分析表明，当点扩展函数的标准差在160 nm时，有效像元大小在120、160、200 nm能取得较好的重构效果，而在60 nm时效果较差。探测器收集的光子数越多，重构效果越好，随着背景信号光子数增加时，离得越近的样品结构越不能分辨。在同样的分块处理情况下，MMV-CS比同伦算法(L1-Homotopy, L1-H）和凸优化算法(CVX)分别快一个数量级和三个数量级，因此，在研究三维超分辨荧光显微成像时，MMV-CS算法在运行时间上具有更大的优势。

Research on super-resolution fluorescence microscopy imaging based on multiple measurement vector compressed sensing

In the super-resolution microscopy imaging technology, single molecule localization microscopy is one of the widely used techniques. In this paper, in order to achieve super-resolution fluorescence image reconstruction, a multiple measurement vector Compressed sensing (MMV-CS) model was established based on the principle of fluorescence microscopic imaging, and the multiple sparse Bayesian learning algorithm was applied in problem solving. The effects of the effective pixel size, the number of photons generated by fluorescent molecules and the Poisson noise of fluorescence and background signal on the reconstruction results were analyzed. The running time of the algorithm was analyzed with the image subdivided into smaller patches. The results of simulation and experimental calculation show that when the standard deviation of the point spread function is 160 nm, the effective pixel size at 120 nm, 160 nm and 200 nm can achieve good reconstruction effect, while the pixel size at 60 nm results in poor effect. Better reconstruction image quality is achieved with more photons collected by the detector. As the background signal photons increase, the sample structure becomes indistinguishable when the distance is too close. Under the same subdivided condition, MMV-CS is one order of magnitude faster than the Homotopy (L1-H) algorithm and three orders of magnitude faster than the convex optimization algorithm (CVX), which has greater advantages in terms of running time for the application of MMV-CS in 3D super-resolution fluorescence microscopy.