Localization microscopy such as STORM/PALM achieves the super-resolution by sparsely activating photo-switchable probes. However, to make the activation sparse enough to obtain reconstruction images using conventional algorithms, only small set of probes need to be activated simultaneously, which limits the temporal resolution. Hence, to improve temporal resolution up to a level of live cell imaging, high-density imaging algorithms that can resolve several overlapping PSFs are required. In this paper, we propose a maximum likelihood algorithm under Poisson noise model for the high-density low-SNR STORM/PALM imaging. Using a sparsity promoting prior with concave-convex procedure (CCCP) optimization algorithm, we achieved high performance reconstructions with fast reconstruction speed of 5 second per frame under high density low SNR imaging conditions. Experimental results using simulated and real live-cell imaging data demonstrate that proposed algorithm is more robust than previous methods in terms of both localization accuracy and molecular recall rate.