High-throughput microscopy in the sense of large areas imaged at high-resolution demands costly hardware such as objective lenses with high numerical aperture and high sensitivity cameras, typically combined with lateral mechanical scanning of the sample. The field of view and the resolution of an imaging system depend strongly on the applied objective lens, with higher resolution coming at the cost of a smaller field of view. To address this limitation of conventional microscopes, both aperture synthesis and phase retrieval techniques are combined in the recent computational imaging approach of Fourier Ptychographic Microscopy (FPM). Gigapixel space-bandwidth product of FPM is obtained by combining low-resolution images obtained with illumination diversity through phase retrieval, which is facilitated by ensuring that the input images overlap in the Fourier domain. In practice, the illumination is achieved using one lamp at a time from an LED array. A drawback of FPM is that it requires long acquisition times and has significant computational cost. Here, we present a refined FPM procedure by using Fresnel propagation and reducing the number of exposures by multiplexing and symmetry considerations, thus slashing the amount of data and the processing time. The multiplexing strategy works by illuminating groups of three LEDs that are chosen from one-half plane of the LED array – an approach valid for pure amplitude samples. We have experimentally demonstrated that the FPM recovered image has approximately the same resolution as recovery based on one exposure from each of the LEDs.