Efficient image reconstruction of high-density molecules with augmented Lagrangian method in super-resolution microscopy.

High-density molecules localization algorithm is crucial to obtain sufficient temporal resolution in super-resolution fluorescence microscopy, particularly in view of the challenges associated with live-cell imaging. In this work, an algorithm based on augmented Lagrangian method (ALM) is proposed for reconstructing high-density molecules. The problem is firstly converted to an equivalent optimization problem with constraints using variable splitting, and then the alternating minimization method is applied to implement it straightforwardly. We also take advantage of quasi-Newton method to tackle the sub-problems for acceleration, and total variation regularization to reduce noise. Numerical results on both simulated and real data demonstrate that the algorithm can achieve using fewer frames of raw images to reconstruct high-resolution image with favorable performance in terms of detection rate and image quality.