Three-dimensional single-molecule localization microscopy imaging based on compressed sensing

In order to achieve fast three-dimensional localization of high-density fluorescent molecular images, a three-dimensional compressed sensing model was established and studied using the CVX method, the Orthogonal Matching Pursuit(OMP) algorithm and a homotopy algorithm. The models’ measurement matrix was then designed. Firstly, the system’s theory and design were both developed using the three-dimensional point-spread function imaging theory of fluorescence microscopy. Then, the process of fluorescence microscopic imaging was simulated, through which the images generated in the established compressed sensing model were analyzed using the CVX method, OMP algorithm and homotopy algorithm. The recall rate, localization accuracy and reconstruction time were compared. Finally, the simulated biological samples and the collected cells in the laboratory were analyzed using the homotopy algorithm, and thus three-dimensional super-resolution imaging was achieved. It can be seen from the comparative results that the homotopy algorithm is two orders of magnitude faster than the CVX method when the reconstruction density and localization accuracy have little deviation. The localization accuracy of the homotopy algorithm is twice higher than that of the OMP algorithm. The homotopy algorithm is meaningful for 3D super-resolution fluorescence microscopy imaging, which can save computing time and achieve real-time imaging.