Recently Fourier Ptychography (FP) has attracted great attention, due to its marked effectiveness in leveraging snapshot numbers for spatial resolution in large field-of-view imaging. To acquire high signal-to-noise-ratio (SNR) images under angularly varying illuminations for subsequent reconstruction, FP requires long exposure time, which largely limits its practical applications. In this paper, based on the recently reported Wirtinger flow algorithm, we propose an iterative optimization framework incorporating phase retrieval and noise relaxation together, to realize FP reconstruction using low SNR images captured under short exposure time. Experiments on both synthetic and real captured data validate the effectiveness of the proposed reconstruction method. Specifically, the proposed technique could save ~ 80% exposure time to achieve similar retrieval accuracy compared to the conventional FP. Besides, we have released our source code for non-commercial use.