Fast 3D localization algorithm for high-density molecules based on multiple measurement vector compressed sensing

Abstract Single-molecule localization microscopy (SMLM) achieves super-resolution based on a series of images of sparsely distributed molecules, which makes it time-consuming. To improve the temporal resolution, several high-density localization algorithms have been developed, and the computational speed is considered one of the important factors for evaluating their performance. In this study, for the first time, a three-dimensional (3D) multiple measurement vector compressed sensing (3D-MMV-CS) model was constructed and then solved using a multiple sparse Bayesian learning algorithm to realize 3D single-molecule localization and obtain 3D super-resolved fluorescence images. The 3D-MMV-CS successfully recovered a 3D super-resolved image from a series of simulated high-density fluorescence images. The computation time for reconstruction only increases marginally with an increase in the number of raw images and approximately stays constant with an increase in the density of fluorescent molecules. Simulation results demonstrated that, when the number of raw images reaches 1900, compared with the other two algorithms L1-Homotopy and compressed sensing STORM (CSSTORM) with CVX, the 3D-MMV-CS method is 100 times faster than the former and five orders of magnitude faster than the latter. This outstanding performance in computation speed would allow the 3D-MMV-CS approach to be routinely applicable to SMLM. Validation test of the 3D-MMV-CS method was performed successfully with experimental data from an astigmatism-based 3D SMLM system.