Fast Frequency-Domain Compressed Sensing Analysis for High-Density Super-Resolution Imaging Using Orthogonal Matching Pursuit

Single-molecule localization methods play a vital role in a localization-based super-resolution fluorescence microscopy. However, it is difficult for conventional localization schemes based on the Gaussian fitting to locate overlapped high-density fluorescent emitters. Currently, in the spatial domain, the compressive-sensing-based algorithm (CSSTORM) can localize high-emitter-density images. However, the computational cost of this approach is extremely high, which limits its practical application. Here, we propose an alternative frequency-domain compressed sensing (FD-CS) technique for fast super-resolution imaging. Unlike the CSSTORM method, which is a measurement matrix based on the point spread function, a Fourier dictionary designed in the frequency domain and orthogonal matching pursuit is used to reliably recover the original signal. The simulation and experimental results prove that the FD-CS is 1000 times faster than CSSTORM with CVX and ten times faster than that with L1-Homotopy with almost the same localization accuracy and recall rate. This drastic reduction in computational time should allow the compressed sensing approach to be routinely applied to a super-resolution image analysis.