Light field microscopy is a high-speed 3D imaging technique that records the light field from multiple angles by the microlens array(MLA), thus allowing us to obtain information about the light source from a single image only. For the fundamental problem of neuron localization, we improve the method of combining depth-dependent dictionary with sparse coding in this paper. In order to obtain higher localization accuracy and good noise immunity, we propose an inertial proximal gradient acceleration algorithm with dry friction, Fast-IPGDF. By preventing falling into a local minimum, our algorithm achieves better convergence and converges quite fast, which improves the speed and accuracy of obtaining the locolization of the light source based on the matching depth of epipolar plane images (EPI). We demonstrate the effectiveness of the algorithm for localizing non-scattered fluorescent beads in both noisy and non-noisy environments. The experimental results show that our method can achieve simultaneous localization of multiple point sources and effective localization in noisy environments. Compared to existing studies, our method shows significant improvements in both localization accuracy and speed.